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and-apply-cardinality-every-integer_partitions-integerp-lambda-map-subset

integer_partitions (3);

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cardinality (s);

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and-apply-cardinality-every-integer_partitions-integerp-lambda-map-subset

integer_partitions (4);

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and-apply-cardinality-every-integer_partitions-integerp-lambda-map-subset

integer_partitions (3);

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cardinality (s);

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and-apply-cardinality-every-integer_partitions-integerp-lambda-map-subset

integer_partitions (3);

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cardinality (s);

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and-apply-cardinality-every-integer_partitions-integerp-lambda-map-subset

integer_partitions (20);

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and-apply-cardinality-every-integer_partitions-integerp-lambda-map-subset

integer_partitions (3);

s: integer_partition...

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and-apply-cardinality-every-integer_partitions-integerp-lambda-map-subset

integer_partitions (4);

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cardinality (s);

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and-apply-cardinality-every-integer_partitions-integerp-lambda-map-subset

integer_partitions (4);

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cardinality (s);

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and-apply-cardinality-every-integer_partitions-integerp-lambda-map-subset

integer_partitions (3);

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cardinality (s);

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and-apply-cardinality-every-integer_partitions-integerp-lambda-map-subset

integer_partitions (4);

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Run Example
(%i1)integer_partitions (3);
(%o1)                      {[1, 1, 1], [2, 1], [3]}
(%i2)  s: integer_partitions (21);
(%o2) {[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], 
[2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1], 
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1], [3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1], [3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1], 
[3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1], [3, 2, 2, 2, 2, 2, 2, 2, 2, 2], 
[3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1], 
[3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1], [3, 3, 2, 2, 2, 2, 2, 2, 2, 1], 
[3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1], 
[3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1], [3, 3, 3, 2, 2, 2, 2, 2, 1, 1], 
[3, 3, 3, 2, 2, 2, 2, 2, 2], [3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1], [3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1], 
[3, 3, 3, 3, 2, 2, 2, 1, 1, 1], [3, 3, 3, 3, 2, 2, 2, 2, 1], 
[3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1], [3, 3, 3, 3, 3, 2, 1, 1, 1, 1], 
[3, 3, 3, 3, 3, 2, 2, 1, 1], [3, 3, 3, 3, 3, 2, 2, 2], 
[3, 3, 3, 3, 3, 3, 1, 1, 1], [3, 3, 3, 3, 3, 3, 2, 1], [3, 3, 3, 3, 3, 3, 3], 
[4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [4, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1], 
[4, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1], [4, 2, 2, 2, 2, 2, 2, 2, 2, 1], 
[4, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [4, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1], 
[4, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1], [4, 3, 2, 2, 2, 2, 2, 2, 1, 1], 
[4, 3, 2, 2, 2, 2, 2, 2, 2], [4, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1], 
[4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1], [4, 3, 3, 2, 2, 2, 2, 1, 1, 1], 
[4, 3, 3, 2, 2, 2, 2, 2, 1], [4, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1], [4, 3, 3, 3, 2, 2, 1, 1, 1, 1], 
[4, 3, 3, 3, 2, 2, 2, 1, 1], [4, 3, 3, 3, 2, 2, 2, 2], 
[4, 3, 3, 3, 3, 1, 1, 1, 1, 1], [4, 3, 3, 3, 3, 2, 1, 1, 1], 
[4, 3, 3, 3, 3, 2, 2, 1], [4, 3, 3, 3, 3, 3, 1, 1], [4, 3, 3, 3, 3, 3, 2], 
[4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], 
[4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1], [4, 4, 2, 2, 2, 2, 2, 1, 1, 1], 
[4, 4, 2, 2, 2, 2, 2, 2, 1], [4, 4, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1], 
[4, 4, 3, 2, 2, 2, 1, 1, 1, 1], [4, 4, 3, 2, 2, 2, 2, 1, 1], 
[4, 4, 3, 2, 2, 2, 2, 2], [4, 4, 3, 3, 1, 1, 1, 1, 1, 1, 1], 
[4, 4, 3, 3, 2, 1, 1, 1, 1, 1], [4, 4, 3, 3, 2, 2, 1, 1, 1], 
[4, 4, 3, 3, 2, 2, 2, 1], [4, 4, 3, 3, 3, 1, 1, 1, 1], 
[4, 4, 3, 3, 3, 2, 1, 1], [4, 4, 3, 3, 3, 2, 2], [4, 4, 3, 3, 3, 3, 1], 
[4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 2, 1, 1, 1, 1, 1, 1, 1], 
[4, 4, 4, 2, 2, 1, 1, 1, 1, 1], [4, 4, 4, 2, 2, 2, 1, 1, 1], 
[4, 4, 4, 2, 2, 2, 2, 1], [4, 4, 4, 3, 1, 1, 1, 1, 1, 1], 
[4, 4, 4, 3, 2, 1, 1, 1, 1], [4, 4, 4, 3, 2, 2, 1, 1], [4, 4, 4, 3, 2, 2, 2], 
[4, 4, 4, 3, 3, 1, 1, 1], [4, 4, 4, 3, 3, 2, 1], [4, 4, 4, 3, 3, 3], 
[4, 4, 4, 4, 1, 1, 1, 1, 1], [4, 4, 4, 4, 2, 1, 1, 1], [4, 4, 4, 4, 2, 2, 1], 
[4, 4, 4, 4, 3, 1, 1], [4, 4, 4, 4, 3, 2], [4, 4, 4, 4, 4, 1], 
[5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[5, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[5, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[5, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[5, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [5, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1], 
[5, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1], [5, 2, 2, 2, 2, 2, 2, 2, 1, 1], 
[5, 2, 2, 2, 2, 2, 2, 2, 2], [5, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[5, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[5, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], 
[5, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1], [5, 3, 2, 2, 2, 2, 2, 1, 1, 1], 
[5, 3, 2, 2, 2, 2, 2, 2, 1], [5, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[5, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1], [5, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1], 
[5, 3, 3, 2, 2, 2, 1, 1, 1, 1], [5, 3, 3, 2, 2, 2, 2, 1, 1], 
[5, 3, 3, 2, 2, 2, 2, 2], [5, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1], 
[5, 3, 3, 3, 2, 1, 1, 1, 1, 1], [5, 3, 3, 3, 2, 2, 1, 1, 1], 
[5, 3, 3, 3, 2, 2, 2, 1], [5, 3, 3, 3, 3, 1, 1, 1, 1], 
[5, 3, 3, 3, 3, 2, 1, 1], [5, 3, 3, 3, 3, 2, 2], [5, 3, 3, 3, 3, 3, 1], 
[5, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[5, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], 
[5, 4, 2, 2, 2, 1, 1, 1, 1, 1, 1], [5, 4, 2, 2, 2, 2, 1, 1, 1, 1], 
[5, 4, 2, 2, 2, 2, 2, 1, 1], [5, 4, 2, 2, 2, 2, 2, 2], 
[5, 4, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1], 
[5, 4, 3, 2, 2, 1, 1, 1, 1, 1], [5, 4, 3, 2, 2, 2, 1, 1, 1], 
[5, 4, 3, 2, 2, 2, 2, 1], [5, 4, 3, 3, 1, 1, 1, 1, 1, 1], 
[5, 4, 3, 3, 2, 1, 1, 1, 1], [5, 4, 3, 3, 2, 2, 1, 1], [5, 4, 3, 3, 2, 2, 2], 
[5, 4, 3, 3, 3, 1, 1, 1], [5, 4, 3, 3, 3, 2, 1], [5, 4, 3, 3, 3, 3], 
[5, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 4, 2, 1, 1, 1, 1, 1, 1], 
[5, 4, 4, 2, 2, 1, 1, 1, 1], [5, 4, 4, 2, 2, 2, 1, 1], [5, 4, 4, 2, 2, 2, 2], 
[5, 4, 4, 3, 1, 1, 1, 1, 1], [5, 4, 4, 3, 2, 1, 1, 1], [5, 4, 4, 3, 2, 2, 1], 
[5, 4, 4, 3, 3, 1, 1], [5, 4, 4, 3, 3, 2], [5, 4, 4, 4, 1, 1, 1, 1], 
[5, 4, 4, 4, 2, 1, 1], [5, 4, 4, 4, 2, 2], [5, 4, 4, 4, 3, 1], 
[5, 4, 4, 4, 4], [5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[5, 5, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 5, 2, 2, 1, 1, 1, 1, 1, 1, 1], 
[5, 5, 2, 2, 2, 1, 1, 1, 1, 1], [5, 5, 2, 2, 2, 2, 1, 1, 1], 
[5, 5, 2, 2, 2, 2, 2, 1], [5, 5, 3, 1, 1, 1, 1, 1, 1, 1, 1], 
[5, 5, 3, 2, 1, 1, 1, 1, 1, 1], [5, 5, 3, 2, 2, 1, 1, 1, 1], 
[5, 5, 3, 2, 2, 2, 1, 1], [5, 5, 3, 2, 2, 2, 2], [5, 5, 3, 3, 1, 1, 1, 1, 1], 
[5, 5, 3, 3, 2, 1, 1, 1], [5, 5, 3, 3, 2, 2, 1], [5, 5, 3, 3, 3, 1, 1], 
[5, 5, 3, 3, 3, 2], [5, 5, 4, 1, 1, 1, 1, 1, 1, 1], 
[5, 5, 4, 2, 1, 1, 1, 1, 1], [5, 5, 4, 2, 2, 1, 1, 1], [5, 5, 4, 2, 2, 2, 1], 
[5, 5, 4, 3, 1, 1, 1, 1], [5, 5, 4, 3, 2, 1, 1], [5, 5, 4, 3, 2, 2], 
[5, 5, 4, 3, 3, 1], [5, 5, 4, 4, 1, 1, 1], [5, 5, 4, 4, 2, 1], 
[5, 5, 4, 4, 3], [5, 5, 5, 1, 1, 1, 1, 1, 1], [5, 5, 5, 2, 1, 1, 1, 1], 
[5, 5, 5, 2, 2, 1, 1], [5, 5, 5, 2, 2, 2], [5, 5, 5, 3, 1, 1, 1], 
[5, 5, 5, 3, 2, 1], [5, 5, 5, 3, 3], [5, 5, 5, 4, 1, 1], [5, 5, 5, 4, 2], 
[5, 5, 5, 5, 1], [6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[6, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[6, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[6, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [6, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], 
[6, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1], [6, 2, 2, 2, 2, 2, 2, 1, 1, 1], 
[6, 2, 2, 2, 2, 2, 2, 2, 1], [6, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[6, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [6, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], 
[6, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1], [6, 3, 2, 2, 2, 2, 1, 1, 1, 1], 
[6, 3, 2, 2, 2, 2, 2, 1, 1], [6, 3, 2, 2, 2, 2, 2, 2], 
[6, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [6, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1], 
[6, 3, 3, 2, 2, 1, 1, 1, 1, 1], [6, 3, 3, 2, 2, 2, 1, 1, 1], 
[6, 3, 3, 2, 2, 2, 2, 1], [6, 3, 3, 3, 1, 1, 1, 1, 1, 1], 
[6, 3, 3, 3, 2, 1, 1, 1, 1], [6, 3, 3, 3, 2, 2, 1, 1], [6, 3, 3, 3, 2, 2, 2], 
[6, 3, 3, 3, 3, 1, 1, 1], [6, 3, 3, 3, 3, 2, 1], [6, 3, 3, 3, 3, 3], 
[6, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [6, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[6, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1], [6, 4, 2, 2, 2, 1, 1, 1, 1, 1], 
[6, 4, 2, 2, 2, 2, 1, 1, 1], [6, 4, 2, 2, 2, 2, 2, 1], 
[6, 4, 3, 1, 1, 1, 1, 1, 1, 1, 1], [6, 4, 3, 2, 1, 1, 1, 1, 1, 1], 
[6, 4, 3, 2, 2, 1, 1, 1, 1], [6, 4, 3, 2, 2, 2, 1, 1], [6, 4, 3, 2, 2, 2, 2], 
[6, 4, 3, 3, 1, 1, 1, 1, 1], [6, 4, 3, 3, 2, 1, 1, 1], [6, 4, 3, 3, 2, 2, 1], 
[6, 4, 3, 3, 3, 1, 1], [6, 4, 3, 3, 3, 2], [6, 4, 4, 1, 1, 1, 1, 1, 1, 1], 
[6, 4, 4, 2, 1, 1, 1, 1, 1], [6, 4, 4, 2, 2, 1, 1, 1], [6, 4, 4, 2, 2, 2, 1], 
[6, 4, 4, 3, 1, 1, 1, 1], [6, 4, 4, 3, 2, 1, 1], [6, 4, 4, 3, 2, 2], 
[6, 4, 4, 3, 3, 1], [6, 4, 4, 4, 1, 1, 1], [6, 4, 4, 4, 2, 1], 
[6, 4, 4, 4, 3], [6, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[6, 5, 2, 1, 1, 1, 1, 1, 1, 1, 1], [6, 5, 2, 2, 1, 1, 1, 1, 1, 1], 
[6, 5, 2, 2, 2, 1, 1, 1, 1], [6, 5, 2, 2, 2, 2, 1, 1], [6, 5, 2, 2, 2, 2, 2], 
[6, 5, 3, 1, 1, 1, 1, 1, 1, 1], [6, 5, 3, 2, 1, 1, 1, 1, 1], 
[6, 5, 3, 2, 2, 1, 1, 1], [6, 5, 3, 2, 2, 2, 1], [6, 5, 3, 3, 1, 1, 1, 1], 
[6, 5, 3, 3, 2, 1, 1], [6, 5, 3, 3, 2, 2], [6, 5, 3, 3, 3, 1], 
[6, 5, 4, 1, 1, 1, 1, 1, 1], [6, 5, 4, 2, 1, 1, 1, 1], [6, 5, 4, 2, 2, 1, 1], 
[6, 5, 4, 2, 2, 2], [6, 5, 4, 3, 1, 1, 1], [6, 5, 4, 3, 2, 1], 
[6, 5, 4, 3, 3], [6, 5, 4, 4, 1, 1], [6, 5, 4, 4, 2], 
[6, 5, 5, 1, 1, 1, 1, 1], [6, 5, 5, 2, 1, 1, 1], [6, 5, 5, 2, 2, 1], 
[6, 5, 5, 3, 1, 1], [6, 5, 5, 3, 2], [6, 5, 5, 4, 1], [6, 5, 5, 5], 
[6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1], [6, 6, 2, 1, 1, 1, 1, 1, 1, 1], 
[6, 6, 2, 2, 1, 1, 1, 1, 1], [6, 6, 2, 2, 2, 1, 1, 1], [6, 6, 2, 2, 2, 2, 1], 
[6, 6, 3, 1, 1, 1, 1, 1, 1], [6, 6, 3, 2, 1, 1, 1, 1], [6, 6, 3, 2, 2, 1, 1], 
[6, 6, 3, 2, 2, 2], [6, 6, 3, 3, 1, 1, 1], [6, 6, 3, 3, 2, 1], 
[6, 6, 3, 3, 3], [6, 6, 4, 1, 1, 1, 1, 1], [6, 6, 4, 2, 1, 1, 1], 
[6, 6, 4, 2, 2, 1], [6, 6, 4, 3, 1, 1], [6, 6, 4, 3, 2], [6, 6, 4, 4, 1], 
[6, 6, 5, 1, 1, 1, 1], [6, 6, 5, 2, 1, 1], [6, 6, 5, 2, 2], [6, 6, 5, 3, 1], 
[6, 6, 5, 4], [6, 6, 6, 1, 1, 1], [6, 6, 6, 2, 1], [6, 6, 6, 3], 
[7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[7, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[7, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], 
[7, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1], [7, 2, 2, 2, 2, 2, 1, 1, 1, 1], 
[7, 2, 2, 2, 2, 2, 2, 1, 1], [7, 2, 2, 2, 2, 2, 2, 2], 
[7, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[7, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1], [7, 3, 2, 2, 2, 1, 1, 1, 1, 1], 
[7, 3, 2, 2, 2, 2, 1, 1, 1], [7, 3, 2, 2, 2, 2, 2, 1], 
[7, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1], [7, 3, 3, 2, 1, 1, 1, 1, 1, 1], 
[7, 3, 3, 2, 2, 1, 1, 1, 1], [7, 3, 3, 2, 2, 2, 1, 1], [7, 3, 3, 2, 2, 2, 2], 
[7, 3, 3, 3, 1, 1, 1, 1, 1], [7, 3, 3, 3, 2, 1, 1, 1], [7, 3, 3, 3, 2, 2, 1], 
[7, 3, 3, 3, 3, 1, 1], [7, 3, 3, 3, 3, 2], 
[7, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1], 
[7, 4, 2, 2, 1, 1, 1, 1, 1, 1], [7, 4, 2, 2, 2, 1, 1, 1, 1], 
[7, 4, 2, 2, 2, 2, 1, 1], [7, 4, 2, 2, 2, 2, 2], 
[7, 4, 3, 1, 1, 1, 1, 1, 1, 1], [7, 4, 3, 2, 1, 1, 1, 1, 1], 
[7, 4, 3, 2, 2, 1, 1, 1], [7, 4, 3, 2, 2, 2, 1], [7, 4, 3, 3, 1, 1, 1, 1], 
[7, 4, 3, 3, 2, 1, 1], [7, 4, 3, 3, 2, 2], [7, 4, 3, 3, 3, 1], 
[7, 4, 4, 1, 1, 1, 1, 1, 1], [7, 4, 4, 2, 1, 1, 1, 1], [7, 4, 4, 2, 2, 1, 1], 
[7, 4, 4, 2, 2, 2], [7, 4, 4, 3, 1, 1, 1], [7, 4, 4, 3, 2, 1], 
[7, 4, 4, 3, 3], [7, 4, 4, 4, 1, 1], [7, 4, 4, 4, 2], 
[7, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 5, 2, 1, 1, 1, 1, 1, 1, 1], 
[7, 5, 2, 2, 1, 1, 1, 1, 1], [7, 5, 2, 2, 2, 1, 1, 1], [7, 5, 2, 2, 2, 2, 1], 
[7, 5, 3, 1, 1, 1, 1, 1, 1], [7, 5, 3, 2, 1, 1, 1, 1], [7, 5, 3, 2, 2, 1, 1], 
[7, 5, 3, 2, 2, 2], [7, 5, 3, 3, 1, 1, 1], [7, 5, 3, 3, 2, 1], 
[7, 5, 3, 3, 3], [7, 5, 4, 1, 1, 1, 1, 1], [7, 5, 4, 2, 1, 1, 1], 
[7, 5, 4, 2, 2, 1], [7, 5, 4, 3, 1, 1], [7, 5, 4, 3, 2], [7, 5, 4, 4, 1], 
[7, 5, 5, 1, 1, 1, 1], [7, 5, 5, 2, 1, 1], [7, 5, 5, 2, 2], [7, 5, 5, 3, 1], 
[7, 5, 5, 4], [7, 6, 1, 1, 1, 1, 1, 1, 1, 1], [7, 6, 2, 1, 1, 1, 1, 1, 1], 
[7, 6, 2, 2, 1, 1, 1, 1], [7, 6, 2, 2, 2, 1, 1], [7, 6, 2, 2, 2, 2], 
[7, 6, 3, 1, 1, 1, 1, 1], [7, 6, 3, 2, 1, 1, 1], [7, 6, 3, 2, 2, 1], 
[7, 6, 3, 3, 1, 1], [7, 6, 3, 3, 2], [7, 6, 4, 1, 1, 1, 1], 
[7, 6, 4, 2, 1, 1], [7, 6, 4, 2, 2], [7, 6, 4, 3, 1], [7, 6, 4, 4], 
[7, 6, 5, 1, 1, 1], [7, 6, 5, 2, 1], [7, 6, 5, 3], [7, 6, 6, 1, 1], 
[7, 6, 6, 2], [7, 7, 1, 1, 1, 1, 1, 1, 1], [7, 7, 2, 1, 1, 1, 1, 1], 
[7, 7, 2, 2, 1, 1, 1], [7, 7, 2, 2, 2, 1], [7, 7, 3, 1, 1, 1, 1], 
[7, 7, 3, 2, 1, 1], [7, 7, 3, 2, 2], [7, 7, 3, 3, 1], [7, 7, 4, 1, 1, 1], 
[7, 7, 4, 2, 1], [7, 7, 4, 3], [7, 7, 5, 1, 1], [7, 7, 5, 2], [7, 7, 6, 1], 
[7, 7, 7], [8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[8, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[8, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [8, 2, 2, 2, 2, 1, 1, 1, 1, 1], 
[8, 2, 2, 2, 2, 2, 1, 1, 1], [8, 2, 2, 2, 2, 2, 2, 1], 
[8, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1], 
[8, 3, 2, 2, 1, 1, 1, 1, 1, 1], [8, 3, 2, 2, 2, 1, 1, 1, 1], 
[8, 3, 2, 2, 2, 2, 1, 1], [8, 3, 2, 2, 2, 2, 2], 
[8, 3, 3, 1, 1, 1, 1, 1, 1, 1], [8, 3, 3, 2, 1, 1, 1, 1, 1], 
[8, 3, 3, 2, 2, 1, 1, 1], [8, 3, 3, 2, 2, 2, 1], [8, 3, 3, 3, 1, 1, 1, 1], 
[8, 3, 3, 3, 2, 1, 1], [8, 3, 3, 3, 2, 2], [8, 3, 3, 3, 3, 1], 
[8, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 4, 2, 1, 1, 1, 1, 1, 1, 1], 
[8, 4, 2, 2, 1, 1, 1, 1, 1], [8, 4, 2, 2, 2, 1, 1, 1], [8, 4, 2, 2, 2, 2, 1], 
[8, 4, 3, 1, 1, 1, 1, 1, 1], [8, 4, 3, 2, 1, 1, 1, 1], [8, 4, 3, 2, 2, 1, 1], 
[8, 4, 3, 2, 2, 2], [8, 4, 3, 3, 1, 1, 1], [8, 4, 3, 3, 2, 1], 
[8, 4, 3, 3, 3], [8, 4, 4, 1, 1, 1, 1, 1], [8, 4, 4, 2, 1, 1, 1], 
[8, 4, 4, 2, 2, 1], [8, 4, 4, 3, 1, 1], [8, 4, 4, 3, 2], [8, 4, 4, 4, 1], 
[8, 5, 1, 1, 1, 1, 1, 1, 1, 1], [8, 5, 2, 1, 1, 1, 1, 1, 1], 
[8, 5, 2, 2, 1, 1, 1, 1], [8, 5, 2, 2, 2, 1, 1], [8, 5, 2, 2, 2, 2], 
[8, 5, 3, 1, 1, 1, 1, 1], [8, 5, 3, 2, 1, 1, 1], [8, 5, 3, 2, 2, 1], 
[8, 5, 3, 3, 1, 1], [8, 5, 3, 3, 2], [8, 5, 4, 1, 1, 1, 1], 
[8, 5, 4, 2, 1, 1], [8, 5, 4, 2, 2], [8, 5, 4, 3, 1], [8, 5, 4, 4], 
[8, 5, 5, 1, 1, 1], [8, 5, 5, 2, 1], [8, 5, 5, 3], 
[8, 6, 1, 1, 1, 1, 1, 1, 1], [8, 6, 2, 1, 1, 1, 1, 1], [8, 6, 2, 2, 1, 1, 1], 
[8, 6, 2, 2, 2, 1], [8, 6, 3, 1, 1, 1, 1], [8, 6, 3, 2, 1, 1], 
[8, 6, 3, 2, 2], [8, 6, 3, 3, 1], [8, 6, 4, 1, 1, 1], [8, 6, 4, 2, 1], 
[8, 6, 4, 3], [8, 6, 5, 1, 1], [8, 6, 5, 2], [8, 6, 6, 1], 
[8, 7, 1, 1, 1, 1, 1, 1], [8, 7, 2, 1, 1, 1, 1], [8, 7, 2, 2, 1, 1], 
[8, 7, 2, 2, 2], [8, 7, 3, 1, 1, 1], [8, 7, 3, 2, 1], [8, 7, 3, 3], 
[8, 7, 4, 1, 1], [8, 7, 4, 2], [8, 7, 5, 1], [8, 7, 6], [8, 8, 1, 1, 1, 1, 1], 
[8, 8, 2, 1, 1, 1], [8, 8, 2, 2, 1], [8, 8, 3, 1, 1], [8, 8, 3, 2], 
[8, 8, 4, 1], [8, 8, 5], [9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[9, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [9, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], 
[9, 2, 2, 2, 1, 1, 1, 1, 1, 1], [9, 2, 2, 2, 2, 1, 1, 1, 1], 
[9, 2, 2, 2, 2, 2, 1, 1], [9, 2, 2, 2, 2, 2, 2], 
[9, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [9, 3, 2, 1, 1, 1, 1, 1, 1, 1], 
[9, 3, 2, 2, 1, 1, 1, 1, 1], [9, 3, 2, 2, 2, 1, 1, 1], [9, 3, 2, 2, 2, 2, 1], 
[9, 3, 3, 1, 1, 1, 1, 1, 1], [9, 3, 3, 2, 1, 1, 1, 1], [9, 3, 3, 2, 2, 1, 1], 
[9, 3, 3, 2, 2, 2], [9, 3, 3, 3, 1, 1, 1], [9, 3, 3, 3, 2, 1], 
[9, 3, 3, 3, 3], [9, 4, 1, 1, 1, 1, 1, 1, 1, 1], [9, 4, 2, 1, 1, 1, 1, 1, 1], 
[9, 4, 2, 2, 1, 1, 1, 1], [9, 4, 2, 2, 2, 1, 1], [9, 4, 2, 2, 2, 2], 
[9, 4, 3, 1, 1, 1, 1, 1], [9, 4, 3, 2, 1, 1, 1], [9, 4, 3, 2, 2, 1], 
[9, 4, 3, 3, 1, 1], [9, 4, 3, 3, 2], [9, 4, 4, 1, 1, 1, 1], 
[9, 4, 4, 2, 1, 1], [9, 4, 4, 2, 2], [9, 4, 4, 3, 1], [9, 4, 4, 4], 
[9, 5, 1, 1, 1, 1, 1, 1, 1], [9, 5, 2, 1, 1, 1, 1, 1], [9, 5, 2, 2, 1, 1, 1], 
[9, 5, 2, 2, 2, 1], [9, 5, 3, 1, 1, 1, 1], [9, 5, 3, 2, 1, 1], 
[9, 5, 3, 2, 2], [9, 5, 3, 3, 1], [9, 5, 4, 1, 1, 1], [9, 5, 4, 2, 1], 
[9, 5, 4, 3], [9, 5, 5, 1, 1], [9, 5, 5, 2], [9, 6, 1, 1, 1, 1, 1, 1], 
[9, 6, 2, 1, 1, 1, 1], [9, 6, 2, 2, 1, 1], [9, 6, 2, 2, 2], 
[9, 6, 3, 1, 1, 1], [9, 6, 3, 2, 1], [9, 6, 3, 3], [9, 6, 4, 1, 1], 
[9, 6, 4, 2], [9, 6, 5, 1], [9, 6, 6], [9, 7, 1, 1, 1, 1, 1], 
[9, 7, 2, 1, 1, 1], [9, 7, 2, 2, 1], [9, 7, 3, 1, 1], [9, 7, 3, 2], 
[9, 7, 4, 1], [9, 7, 5], [9, 8, 1, 1, 1, 1], [9, 8, 2, 1, 1], [9, 8, 2, 2], 
[9, 8, 3, 1], [9, 8, 4], [9, 9, 1, 1, 1], [9, 9, 2, 1], [9, 9, 3], 
[10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [10, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[10, 2, 2, 1, 1, 1, 1, 1, 1, 1], [10, 2, 2, 2, 1, 1, 1, 1, 1], 
[10, 2, 2, 2, 2, 1, 1, 1], [10, 2, 2, 2, 2, 2, 1], 
[10, 3, 1, 1, 1, 1, 1, 1, 1, 1], [10, 3, 2, 1, 1, 1, 1, 1, 1], 
[10, 3, 2, 2, 1, 1, 1, 1], [10, 3, 2, 2, 2, 1, 1], [10, 3, 2, 2, 2, 2], 
[10, 3, 3, 1, 1, 1, 1, 1], [10, 3, 3, 2, 1, 1, 1], [10, 3, 3, 2, 2, 1], 
[10, 3, 3, 3, 1, 1], [10, 3, 3, 3, 2], [10, 4, 1, 1, 1, 1, 1, 1, 1], 
[10, 4, 2, 1, 1, 1, 1, 1], [10, 4, 2, 2, 1, 1, 1], [10, 4, 2, 2, 2, 1], 
[10, 4, 3, 1, 1, 1, 1], [10, 4, 3, 2, 1, 1], [10, 4, 3, 2, 2], 
[10, 4, 3, 3, 1], [10, 4, 4, 1, 1, 1], [10, 4, 4, 2, 1], [10, 4, 4, 3], 
[10, 5, 1, 1, 1, 1, 1, 1], [10, 5, 2, 1, 1, 1, 1], [10, 5, 2, 2, 1, 1], 
[10, 5, 2, 2, 2], [10, 5, 3, 1, 1, 1], [10, 5, 3, 2, 1], [10, 5, 3, 3], 
[10, 5, 4, 1, 1], [10, 5, 4, 2], [10, 5, 5, 1], [10, 6, 1, 1, 1, 1, 1], 
[10, 6, 2, 1, 1, 1], [10, 6, 2, 2, 1], [10, 6, 3, 1, 1], [10, 6, 3, 2], 
[10, 6, 4, 1], [10, 6, 5], [10, 7, 1, 1, 1, 1], [10, 7, 2, 1, 1], 
[10, 7, 2, 2], [10, 7, 3, 1], [10, 7, 4], [10, 8, 1, 1, 1], [10, 8, 2, 1], 
[10, 8, 3], [10, 9, 1, 1], [10, 9, 2], [10, 10, 1], 
[11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [11, 2, 1, 1, 1, 1, 1, 1, 1, 1], 
[11, 2, 2, 1, 1, 1, 1, 1, 1], [11, 2, 2, 2, 1, 1, 1, 1], 
[11, 2, 2, 2, 2, 1, 1], [11, 2, 2, 2, 2, 2], [11, 3, 1, 1, 1, 1, 1, 1, 1], 
[11, 3, 2, 1, 1, 1, 1, 1], [11, 3, 2, 2, 1, 1, 1], [11, 3, 2, 2, 2, 1], 
[11, 3, 3, 1, 1, 1, 1], [11, 3, 3, 2, 1, 1], [11, 3, 3, 2, 2], 
[11, 3, 3, 3, 1], [11, 4, 1, 1, 1, 1, 1, 1], [11, 4, 2, 1, 1, 1, 1], 
[11, 4, 2, 2, 1, 1], [11, 4, 2, 2, 2], [11, 4, 3, 1, 1, 1], [11, 4, 3, 2, 1], 
[11, 4, 3, 3], [11, 4, 4, 1, 1], [11, 4, 4, 2], [11, 5, 1, 1, 1, 1, 1], 
[11, 5, 2, 1, 1, 1], [11, 5, 2, 2, 1], [11, 5, 3, 1, 1], [11, 5, 3, 2], 
[11, 5, 4, 1], [11, 5, 5], [11, 6, 1, 1, 1, 1], [11, 6, 2, 1, 1], 
[11, 6, 2, 2], [11, 6, 3, 1], [11, 6, 4], [11, 7, 1, 1, 1], [11, 7, 2, 1], 
[11, 7, 3], [11, 8, 1, 1], [11, 8, 2], [11, 9, 1], [11, 10], 
[12, 1, 1, 1, 1, 1, 1, 1, 1, 1], [12, 2, 1, 1, 1, 1, 1, 1, 1], 
[12, 2, 2, 1, 1, 1, 1, 1], [12, 2, 2, 2, 1, 1, 1], [12, 2, 2, 2, 2, 1], 
[12, 3, 1, 1, 1, 1, 1, 1], [12, 3, 2, 1, 1, 1, 1], [12, 3, 2, 2, 1, 1], 
[12, 3, 2, 2, 2], [12, 3, 3, 1, 1, 1], [12, 3, 3, 2, 1], [12, 3, 3, 3], 
[12, 4, 1, 1, 1, 1, 1], [12, 4, 2, 1, 1, 1], [12, 4, 2, 2, 1], 
[12, 4, 3, 1, 1], [12, 4, 3, 2], [12, 4, 4, 1], [12, 5, 1, 1, 1, 1], 
[12, 5, 2, 1, 1], [12, 5, 2, 2], [12, 5, 3, 1], [12, 5, 4], [12, 6, 1, 1, 1], 
[12, 6, 2, 1], [12, 6, 3], [12, 7, 1, 1], [12, 7, 2], [12, 8, 1], [12, 9], 
[13, 1, 1, 1, 1, 1, 1, 1, 1], [13, 2, 1, 1, 1, 1, 1, 1], 
[13, 2, 2, 1, 1, 1, 1], [13, 2, 2, 2, 1, 1], [13, 2, 2, 2, 2], 
[13, 3, 1, 1, 1, 1, 1], [13, 3, 2, 1, 1, 1], [13, 3, 2, 2, 1], 
[13, 3, 3, 1, 1], [13, 3, 3, 2], [13, 4, 1, 1, 1, 1], [13, 4, 2, 1, 1], 
[13, 4, 2, 2], [13, 4, 3, 1], [13, 4, 4], [13, 5, 1, 1, 1], [13, 5, 2, 1], 
[13, 5, 3], [13, 6, 1, 1], [13, 6, 2], [13, 7, 1], [13, 8], 
[14, 1, 1, 1, 1, 1, 1, 1], [14, 2, 1, 1, 1, 1, 1], [14, 2, 2, 1, 1, 1], 
[14, 2, 2, 2, 1], [14, 3, 1, 1, 1, 1], [14, 3, 2, 1, 1], [14, 3, 2, 2], 
[14, 3, 3, 1], [14, 4, 1, 1, 1], [14, 4, 2, 1], [14, 4, 3], [14, 5, 1, 1], 
[14, 5, 2], [14, 6, 1], [14, 7], [15, 1, 1, 1, 1, 1, 1], [15, 2, 1, 1, 1, 1], 
[15, 2, 2, 1, 1], [15, 2, 2, 2], [15, 3, 1, 1, 1], [15, 3, 2, 1], [15, 3, 3], 
[15, 4, 1, 1], [15, 4, 2], [15, 5, 1], [15, 6], [16, 1, 1, 1, 1, 1], 
[16, 2, 1, 1, 1], [16, 2, 2, 1], [16, 3, 1, 1], [16, 3, 2], [16, 4, 1], 
[16, 5], [17, 1, 1, 1, 1], [17, 2, 1, 1], [17, 2, 2], [17, 3, 1], [17, 4], 
[18, 1, 1, 1], [18, 2, 1], [18, 3], [19, 1, 1], [19, 2], [20, 1], [21]}
(%i3)  cardinality (s);
(%o3)                                 792
(%i4)  map (lambda ([x], apply ("+", x)), s);
(%o4)                                {21}
(%i5)  integer_partitions (5, 3);
(%o5)       {[2, 2, 1], [3, 1, 1], [3, 2, 0], [4, 1, 0], [5, 0, 0]}
(%i6)  integer_partitions (5, 2);
(%o6)                      {[3, 2], [4, 1], [5, 0]}
(%i7)  s: integer_partitions (10);
(%o7) {[1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1, 1, 1], 
[2, 2, 1, 1, 1, 1, 1, 1], [2, 2, 2, 1, 1, 1, 1], [2, 2, 2, 2, 1, 1], 
[2, 2, 2, 2, 2], [3, 1, 1, 1, 1, 1, 1, 1], [3, 2, 1, 1, 1, 1, 1], 
[3, 2, 2, 1, 1, 1], [3, 2, 2, 2, 1], [3, 3, 1, 1, 1, 1], [3, 3, 2, 1, 1], 
[3, 3, 2, 2], [3, 3, 3, 1], [4, 1, 1, 1, 1, 1, 1], [4, 2, 1, 1, 1, 1], 
[4, 2, 2, 1, 1], [4, 2, 2, 2], [4, 3, 1, 1, 1], [4, 3, 2, 1], [4, 3, 3], 
[4, 4, 1, 1], [4, 4, 2], [5, 1, 1, 1, 1, 1], [5, 2, 1, 1, 1], [5, 2, 2, 1], 
[5, 3, 1, 1], [5, 3, 2], [5, 4, 1], [5, 5], [6, 1, 1, 1, 1], [6, 2, 1, 1], 
[6, 2, 2], [6, 3, 1], [6, 4], [7, 1, 1, 1], [7, 2, 1], [7, 3], [8, 1, 1], 
[8, 2], [9, 1], [10]}
(%i8)  cardinality (s);
(%o8)                                 42
(%i9)  xprimep(x) := integerp(x) and (x >
 1) and primep(x);
(%o9)         xprimep(x) := integerp(x) and (x > 1) and primep(x)
(%i10)  subset (s, lambda ([x], every (xprimep, x)));
(%o10)    {[2, 2, 2, 2, 2], [3, 3, 2, 2], [5, 3, 2], [5, 5], [7, 3]}
(%i11) 
Run Example
integer_partitions (20);
(%o1) {[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], 
[2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1], 
[2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 
[3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1], 
[3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1], [3, 2, 2, 2, 2, 2, 2, 2, 2, 1], 
[3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1], 
[3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1], [3, 3, 2, 2, 2, 2, 2, 2, 1, 1], 
[3, 3, 2, 2, 2, 2, 2, 2, 2], [3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1], 
[3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1], [3, 3, 3, 2, 2, 2, 2, 1, 1, 1], 
[3, 3, 3, 2, 2, 2, 2, 2, 1], [3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1], [3, 3, 3, 3, 2, 2, 1, 1, 1, 1], 
[3, 3, 3, 3, 2, 2, 2, 1, 1], [3, 3, 3, 3, 2, 2, 2, 2], 
[3, 3, 3, 3, 3, 1, 1, 1, 1, 1], [3, 3, 3, 3, 3, 2, 1, 1, 1], 
[3, 3, 3, 3, 3, 2, 2, 1], [3, 3, 3, 3, 3, 3, 1, 1], [3, 3, 3, 3, 3, 3, 2], 
[4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [4, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1], 
[4, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1], [4, 2, 2, 2, 2, 2, 2, 2, 1, 1], 
[4, 2, 2, 2, 2, 2, 2, 2, 2], [4, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], 
[4, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1], [4, 3, 2, 2, 2, 2, 2, 1, 1, 1], 
[4, 3, 2, 2, 2, 2, 2, 2, 1], [4, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1], [4, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1], 
[4, 3, 3, 2, 2, 2, 1, 1, 1, 1], [4, 3, 3, 2, 2, 2, 2, 1, 1], 
[4, 3, 3, 2, 2, 2, 2, 2], [4, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1], 
[4, 3, 3, 3, 2, 1, 1, 1, 1, 1], [4, 3, 3, 3, 2, 2, 1, 1, 1], 
[4, 3, 3, 3, 2, 2, 2, 1], [4, 3, 3, 3, 3, 1, 1, 1, 1], 
[4, 3, 3, 3, 3, 2, 1, 1], [4, 3, 3, 3, 3, 2, 2], [4, 3, 3, 3, 3, 3, 1], 
[4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 4, 2, 2, 2, 1, 1, 1, 1, 1, 1], [4, 4, 2, 2, 2, 2, 1, 1, 1, 1], 
[4, 4, 2, 2, 2, 2, 2, 1, 1], [4, 4, 2, 2, 2, 2, 2, 2], 
[4, 4, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1], 
[4, 4, 3, 2, 2, 1, 1, 1, 1, 1], [4, 4, 3, 2, 2, 2, 1, 1, 1], 
[4, 4, 3, 2, 2, 2, 2, 1], [4, 4, 3, 3, 1, 1, 1, 1, 1, 1], 
[4, 4, 3, 3, 2, 1, 1, 1, 1], [4, 4, 3, 3, 2, 2, 1, 1], [4, 4, 3, 3, 2, 2, 2], 
[4, 4, 3, 3, 3, 1, 1, 1], [4, 4, 3, 3, 3, 2, 1], [4, 4, 3, 3, 3, 3], 
[4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 2, 1, 1, 1, 1, 1, 1], 
[4, 4, 4, 2, 2, 1, 1, 1, 1], [4, 4, 4, 2, 2, 2, 1, 1], [4, 4, 4, 2, 2, 2, 2], 
[4, 4, 4, 3, 1, 1, 1, 1, 1], [4, 4, 4, 3, 2, 1, 1, 1], [4, 4, 4, 3, 2, 2, 1], 
[4, 4, 4, 3, 3, 1, 1], [4, 4, 4, 3, 3, 2], [4, 4, 4, 4, 1, 1, 1, 1], 
[4, 4, 4, 4, 2, 1, 1], [4, 4, 4, 4, 2, 2], [4, 4, 4, 4, 3, 1], 
[4, 4, 4, 4, 4], [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[5, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[5, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[5, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], 
[5, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1], [5, 2, 2, 2, 2, 2, 2, 1, 1, 1], 
[5, 2, 2, 2, 2, 2, 2, 2, 1], [5, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[5, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], 
[5, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1], [5, 3, 2, 2, 2, 2, 1, 1, 1, 1], 
[5, 3, 2, 2, 2, 2, 2, 1, 1], [5, 3, 2, 2, 2, 2, 2, 2], 
[5, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1], 
[5, 3, 3, 2, 2, 1, 1, 1, 1, 1], [5, 3, 3, 2, 2, 2, 1, 1, 1], 
[5, 3, 3, 2, 2, 2, 2, 1], [5, 3, 3, 3, 1, 1, 1, 1, 1, 1], 
[5, 3, 3, 3, 2, 1, 1, 1, 1], [5, 3, 3, 3, 2, 2, 1, 1], [5, 3, 3, 3, 2, 2, 2], 
[5, 3, 3, 3, 3, 1, 1, 1], [5, 3, 3, 3, 3, 2, 1], [5, 3, 3, 3, 3, 3], 
[5, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[5, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1], [5, 4, 2, 2, 2, 1, 1, 1, 1, 1], 
[5, 4, 2, 2, 2, 2, 1, 1, 1], [5, 4, 2, 2, 2, 2, 2, 1], 
[5, 4, 3, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 3, 2, 1, 1, 1, 1, 1, 1], 
[5, 4, 3, 2, 2, 1, 1, 1, 1], [5, 4, 3, 2, 2, 2, 1, 1], [5, 4, 3, 2, 2, 2, 2], 
[5, 4, 3, 3, 1, 1, 1, 1, 1], [5, 4, 3, 3, 2, 1, 1, 1], [5, 4, 3, 3, 2, 2, 1], 
[5, 4, 3, 3, 3, 1, 1], [5, 4, 3, 3, 3, 2], [5, 4, 4, 1, 1, 1, 1, 1, 1, 1], 
[5, 4, 4, 2, 1, 1, 1, 1, 1], [5, 4, 4, 2, 2, 1, 1, 1], [5, 4, 4, 2, 2, 2, 1], 
[5, 4, 4, 3, 1, 1, 1, 1], [5, 4, 4, 3, 2, 1, 1], [5, 4, 4, 3, 2, 2], 
[5, 4, 4, 3, 3, 1], [5, 4, 4, 4, 1, 1, 1], [5, 4, 4, 4, 2, 1], 
[5, 4, 4, 4, 3], [5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[5, 5, 2, 1, 1, 1, 1, 1, 1, 1, 1], [5, 5, 2, 2, 1, 1, 1, 1, 1, 1], 
[5, 5, 2, 2, 2, 1, 1, 1, 1], [5, 5, 2, 2, 2, 2, 1, 1], [5, 5, 2, 2, 2, 2, 2], 
[5, 5, 3, 1, 1, 1, 1, 1, 1, 1], [5, 5, 3, 2, 1, 1, 1, 1, 1], 
[5, 5, 3, 2, 2, 1, 1, 1], [5, 5, 3, 2, 2, 2, 1], [5, 5, 3, 3, 1, 1, 1, 1], 
[5, 5, 3, 3, 2, 1, 1], [5, 5, 3, 3, 2, 2], [5, 5, 3, 3, 3, 1], 
[5, 5, 4, 1, 1, 1, 1, 1, 1], [5, 5, 4, 2, 1, 1, 1, 1], [5, 5, 4, 2, 2, 1, 1], 
[5, 5, 4, 2, 2, 2], [5, 5, 4, 3, 1, 1, 1], [5, 5, 4, 3, 2, 1], 
[5, 5, 4, 3, 3], [5, 5, 4, 4, 1, 1], [5, 5, 4, 4, 2], 
[5, 5, 5, 1, 1, 1, 1, 1], [5, 5, 5, 2, 1, 1, 1], [5, 5, 5, 2, 2, 1], 
[5, 5, 5, 3, 1, 1], [5, 5, 5, 3, 2], [5, 5, 5, 4, 1], [5, 5, 5, 5], 
[6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[6, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[6, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [6, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], 
[6, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1], [6, 2, 2, 2, 2, 2, 1, 1, 1, 1], 
[6, 2, 2, 2, 2, 2, 2, 1, 1], [6, 2, 2, 2, 2, 2, 2, 2], 
[6, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [6, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[6, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1], [6, 3, 2, 2, 2, 1, 1, 1, 1, 1], 
[6, 3, 2, 2, 2, 2, 1, 1, 1], [6, 3, 2, 2, 2, 2, 2, 1], 
[6, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1], [6, 3, 3, 2, 1, 1, 1, 1, 1, 1], 
[6, 3, 3, 2, 2, 1, 1, 1, 1], [6, 3, 3, 2, 2, 2, 1, 1], [6, 3, 3, 2, 2, 2, 2], 
[6, 3, 3, 3, 1, 1, 1, 1, 1], [6, 3, 3, 3, 2, 1, 1, 1], [6, 3, 3, 3, 2, 2, 1], 
[6, 3, 3, 3, 3, 1, 1], [6, 3, 3, 3, 3, 2], 
[6, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [6, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1], 
[6, 4, 2, 2, 1, 1, 1, 1, 1, 1], [6, 4, 2, 2, 2, 1, 1, 1, 1], 
[6, 4, 2, 2, 2, 2, 1, 1], [6, 4, 2, 2, 2, 2, 2], 
[6, 4, 3, 1, 1, 1, 1, 1, 1, 1], [6, 4, 3, 2, 1, 1, 1, 1, 1], 
[6, 4, 3, 2, 2, 1, 1, 1], [6, 4, 3, 2, 2, 2, 1], [6, 4, 3, 3, 1, 1, 1, 1], 
[6, 4, 3, 3, 2, 1, 1], [6, 4, 3, 3, 2, 2], [6, 4, 3, 3, 3, 1], 
[6, 4, 4, 1, 1, 1, 1, 1, 1], [6, 4, 4, 2, 1, 1, 1, 1], [6, 4, 4, 2, 2, 1, 1], 
[6, 4, 4, 2, 2, 2], [6, 4, 4, 3, 1, 1, 1], [6, 4, 4, 3, 2, 1], 
[6, 4, 4, 3, 3], [6, 4, 4, 4, 1, 1], [6, 4, 4, 4, 2], 
[6, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1], [6, 5, 2, 1, 1, 1, 1, 1, 1, 1], 
[6, 5, 2, 2, 1, 1, 1, 1, 1], [6, 5, 2, 2, 2, 1, 1, 1], [6, 5, 2, 2, 2, 2, 1], 
[6, 5, 3, 1, 1, 1, 1, 1, 1], [6, 5, 3, 2, 1, 1, 1, 1], [6, 5, 3, 2, 2, 1, 1], 
[6, 5, 3, 2, 2, 2], [6, 5, 3, 3, 1, 1, 1], [6, 5, 3, 3, 2, 1], 
[6, 5, 3, 3, 3], [6, 5, 4, 1, 1, 1, 1, 1], [6, 5, 4, 2, 1, 1, 1], 
[6, 5, 4, 2, 2, 1], [6, 5, 4, 3, 1, 1], [6, 5, 4, 3, 2], [6, 5, 4, 4, 1], 
[6, 5, 5, 1, 1, 1, 1], [6, 5, 5, 2, 1, 1], [6, 5, 5, 2, 2], [6, 5, 5, 3, 1], 
[6, 5, 5, 4], [6, 6, 1, 1, 1, 1, 1, 1, 1, 1], [6, 6, 2, 1, 1, 1, 1, 1, 1], 
[6, 6, 2, 2, 1, 1, 1, 1], [6, 6, 2, 2, 2, 1, 1], [6, 6, 2, 2, 2, 2], 
[6, 6, 3, 1, 1, 1, 1, 1], [6, 6, 3, 2, 1, 1, 1], [6, 6, 3, 2, 2, 1], 
[6, 6, 3, 3, 1, 1], [6, 6, 3, 3, 2], [6, 6, 4, 1, 1, 1, 1], 
[6, 6, 4, 2, 1, 1], [6, 6, 4, 2, 2], [6, 6, 4, 3, 1], [6, 6, 4, 4], 
[6, 6, 5, 1, 1, 1], [6, 6, 5, 2, 1], [6, 6, 5, 3], [6, 6, 6, 1, 1], 
[6, 6, 6, 2], [7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[7, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[7, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [7, 2, 2, 2, 2, 1, 1, 1, 1, 1], 
[7, 2, 2, 2, 2, 2, 1, 1, 1], [7, 2, 2, 2, 2, 2, 2, 1], 
[7, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1], 
[7, 3, 2, 2, 1, 1, 1, 1, 1, 1], [7, 3, 2, 2, 2, 1, 1, 1, 1], 
[7, 3, 2, 2, 2, 2, 1, 1], [7, 3, 2, 2, 2, 2, 2], 
[7, 3, 3, 1, 1, 1, 1, 1, 1, 1], [7, 3, 3, 2, 1, 1, 1, 1, 1], 
[7, 3, 3, 2, 2, 1, 1, 1], [7, 3, 3, 2, 2, 2, 1], [7, 3, 3, 3, 1, 1, 1, 1], 
[7, 3, 3, 3, 2, 1, 1], [7, 3, 3, 3, 2, 2], [7, 3, 3, 3, 3, 1], 
[7, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 4, 2, 1, 1, 1, 1, 1, 1, 1], 
[7, 4, 2, 2, 1, 1, 1, 1, 1], [7, 4, 2, 2, 2, 1, 1, 1], [7, 4, 2, 2, 2, 2, 1], 
[7, 4, 3, 1, 1, 1, 1, 1, 1], [7, 4, 3, 2, 1, 1, 1, 1], [7, 4, 3, 2, 2, 1, 1], 
[7, 4, 3, 2, 2, 2], [7, 4, 3, 3, 1, 1, 1], [7, 4, 3, 3, 2, 1], 
[7, 4, 3, 3, 3], [7, 4, 4, 1, 1, 1, 1, 1], [7, 4, 4, 2, 1, 1, 1], 
[7, 4, 4, 2, 2, 1], [7, 4, 4, 3, 1, 1], [7, 4, 4, 3, 2], [7, 4, 4, 4, 1], 
[7, 5, 1, 1, 1, 1, 1, 1, 1, 1], [7, 5, 2, 1, 1, 1, 1, 1, 1], 
[7, 5, 2, 2, 1, 1, 1, 1], [7, 5, 2, 2, 2, 1, 1], [7, 5, 2, 2, 2, 2], 
[7, 5, 3, 1, 1, 1, 1, 1], [7, 5, 3, 2, 1, 1, 1], [7, 5, 3, 2, 2, 1], 
[7, 5, 3, 3, 1, 1], [7, 5, 3, 3, 2], [7, 5, 4, 1, 1, 1, 1], 
[7, 5, 4, 2, 1, 1], [7, 5, 4, 2, 2], [7, 5, 4, 3, 1], [7, 5, 4, 4], 
[7, 5, 5, 1, 1, 1], [7, 5, 5, 2, 1], [7, 5, 5, 3], 
[7, 6, 1, 1, 1, 1, 1, 1, 1], [7, 6, 2, 1, 1, 1, 1, 1], [7, 6, 2, 2, 1, 1, 1], 
[7, 6, 2, 2, 2, 1], [7, 6, 3, 1, 1, 1, 1], [7, 6, 3, 2, 1, 1], 
[7, 6, 3, 2, 2], [7, 6, 3, 3, 1], [7, 6, 4, 1, 1, 1], [7, 6, 4, 2, 1], 
[7, 6, 4, 3], [7, 6, 5, 1, 1], [7, 6, 5, 2], [7, 6, 6, 1], 
[7, 7, 1, 1, 1, 1, 1, 1], [7, 7, 2, 1, 1, 1, 1], [7, 7, 2, 2, 1, 1], 
[7, 7, 2, 2, 2], [7, 7, 3, 1, 1, 1], [7, 7, 3, 2, 1], [7, 7, 3, 3], 
[7, 7, 4, 1, 1], [7, 7, 4, 2], [7, 7, 5, 1], [7, 7, 6], 
[8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[8, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [8, 2, 2, 2, 1, 1, 1, 1, 1, 1], 
[8, 2, 2, 2, 2, 1, 1, 1, 1], [8, 2, 2, 2, 2, 2, 1, 1], [8, 2, 2, 2, 2, 2, 2], 
[8, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 3, 2, 1, 1, 1, 1, 1, 1, 1], 
[8, 3, 2, 2, 1, 1, 1, 1, 1], [8, 3, 2, 2, 2, 1, 1, 1], [8, 3, 2, 2, 2, 2, 1], 
[8, 3, 3, 1, 1, 1, 1, 1, 1], [8, 3, 3, 2, 1, 1, 1, 1], [8, 3, 3, 2, 2, 1, 1], 
[8, 3, 3, 2, 2, 2], [8, 3, 3, 3, 1, 1, 1], [8, 3, 3, 3, 2, 1], 
[8, 3, 3, 3, 3], [8, 4, 1, 1, 1, 1, 1, 1, 1, 1], [8, 4, 2, 1, 1, 1, 1, 1, 1], 
[8, 4, 2, 2, 1, 1, 1, 1], [8, 4, 2, 2, 2, 1, 1], [8, 4, 2, 2, 2, 2], 
[8, 4, 3, 1, 1, 1, 1, 1], [8, 4, 3, 2, 1, 1, 1], [8, 4, 3, 2, 2, 1], 
[8, 4, 3, 3, 1, 1], [8, 4, 3, 3, 2], [8, 4, 4, 1, 1, 1, 1], 
[8, 4, 4, 2, 1, 1], [8, 4, 4, 2, 2], [8, 4, 4, 3, 1], [8, 4, 4, 4], 
[8, 5, 1, 1, 1, 1, 1, 1, 1], [8, 5, 2, 1, 1, 1, 1, 1], [8, 5, 2, 2, 1, 1, 1], 
[8, 5, 2, 2, 2, 1], [8, 5, 3, 1, 1, 1, 1], [8, 5, 3, 2, 1, 1], 
[8, 5, 3, 2, 2], [8, 5, 3, 3, 1], [8, 5, 4, 1, 1, 1], [8, 5, 4, 2, 1], 
[8, 5, 4, 3], [8, 5, 5, 1, 1], [8, 5, 5, 2], [8, 6, 1, 1, 1, 1, 1, 1], 
[8, 6, 2, 1, 1, 1, 1], [8, 6, 2, 2, 1, 1], [8, 6, 2, 2, 2], 
[8, 6, 3, 1, 1, 1], [8, 6, 3, 2, 1], [8, 6, 3, 3], [8, 6, 4, 1, 1], 
[8, 6, 4, 2], [8, 6, 5, 1], [8, 6, 6], [8, 7, 1, 1, 1, 1, 1], 
[8, 7, 2, 1, 1, 1], [8, 7, 2, 2, 1], [8, 7, 3, 1, 1], [8, 7, 3, 2], 
[8, 7, 4, 1], [8, 7, 5], [8, 8, 1, 1, 1, 1], [8, 8, 2, 1, 1], [8, 8, 2, 2], 
[8, 8, 3, 1], [8, 8, 4], [9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[9, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [9, 2, 2, 1, 1, 1, 1, 1, 1, 1], 
[9, 2, 2, 2, 1, 1, 1, 1, 1], [9, 2, 2, 2, 2, 1, 1, 1], [9, 2, 2, 2, 2, 2, 1], 
[9, 3, 1, 1, 1, 1, 1, 1, 1, 1], [9, 3, 2, 1, 1, 1, 1, 1, 1], 
[9, 3, 2, 2, 1, 1, 1, 1], [9, 3, 2, 2, 2, 1, 1], [9, 3, 2, 2, 2, 2], 
[9, 3, 3, 1, 1, 1, 1, 1], [9, 3, 3, 2, 1, 1, 1], [9, 3, 3, 2, 2, 1], 
[9, 3, 3, 3, 1, 1], [9, 3, 3, 3, 2], [9, 4, 1, 1, 1, 1, 1, 1, 1], 
[9, 4, 2, 1, 1, 1, 1, 1], [9, 4, 2, 2, 1, 1, 1], [9, 4, 2, 2, 2, 1], 
[9, 4, 3, 1, 1, 1, 1], [9, 4, 3, 2, 1, 1], [9, 4, 3, 2, 2], [9, 4, 3, 3, 1], 
[9, 4, 4, 1, 1, 1], [9, 4, 4, 2, 1], [9, 4, 4, 3], [9, 5, 1, 1, 1, 1, 1, 1], 
[9, 5, 2, 1, 1, 1, 1], [9, 5, 2, 2, 1, 1], [9, 5, 2, 2, 2], 
[9, 5, 3, 1, 1, 1], [9, 5, 3, 2, 1], [9, 5, 3, 3], [9, 5, 4, 1, 1], 
[9, 5, 4, 2], [9, 5, 5, 1], [9, 6, 1, 1, 1, 1, 1], [9, 6, 2, 1, 1, 1], 
[9, 6, 2, 2, 1], [9, 6, 3, 1, 1], [9, 6, 3, 2], [9, 6, 4, 1], [9, 6, 5], 
[9, 7, 1, 1, 1, 1], [9, 7, 2, 1, 1], [9, 7, 2, 2], [9, 7, 3, 1], [9, 7, 4], 
[9, 8, 1, 1, 1], [9, 8, 2, 1], [9, 8, 3], [9, 9, 1, 1], [9, 9, 2], 
[10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [10, 2, 1, 1, 1, 1, 1, 1, 1, 1], 
[10, 2, 2, 1, 1, 1, 1, 1, 1], [10, 2, 2, 2, 1, 1, 1, 1], 
[10, 2, 2, 2, 2, 1, 1], [10, 2, 2, 2, 2, 2], [10, 3, 1, 1, 1, 1, 1, 1, 1], 
[10, 3, 2, 1, 1, 1, 1, 1], [10, 3, 2, 2, 1, 1, 1], [10, 3, 2, 2, 2, 1], 
[10, 3, 3, 1, 1, 1, 1], [10, 3, 3, 2, 1, 1], [10, 3, 3, 2, 2], 
[10, 3, 3, 3, 1], [10, 4, 1, 1, 1, 1, 1, 1], [10, 4, 2, 1, 1, 1, 1], 
[10, 4, 2, 2, 1, 1], [10, 4, 2, 2, 2], [10, 4, 3, 1, 1, 1], [10, 4, 3, 2, 1], 
[10, 4, 3, 3], [10, 4, 4, 1, 1], [10, 4, 4, 2], [10, 5, 1, 1, 1, 1, 1], 
[10, 5, 2, 1, 1, 1], [10, 5, 2, 2, 1], [10, 5, 3, 1, 1], [10, 5, 3, 2], 
[10, 5, 4, 1], [10, 5, 5], [10, 6, 1, 1, 1, 1], [10, 6, 2, 1, 1], 
[10, 6, 2, 2], [10, 6, 3, 1], [10, 6, 4], [10, 7, 1, 1, 1], [10, 7, 2, 1], 
[10, 7, 3], [10, 8, 1, 1], [10, 8, 2], [10, 9, 1], [10, 10], 
[11, 1, 1, 1, 1, 1, 1, 1, 1, 1], [11, 2, 1, 1, 1, 1, 1, 1, 1], 
[11, 2, 2, 1, 1, 1, 1, 1], [11, 2, 2, 2, 1, 1, 1], [11, 2, 2, 2, 2, 1], 
[11, 3, 1, 1, 1, 1, 1, 1], [11, 3, 2, 1, 1, 1, 1], [11, 3, 2, 2, 1, 1], 
[11, 3, 2, 2, 2], [11, 3, 3, 1, 1, 1], [11, 3, 3, 2, 1], [11, 3, 3, 3], 
[11, 4, 1, 1, 1, 1, 1], [11, 4, 2, 1, 1, 1], [11, 4, 2, 2, 1], 
[11, 4, 3, 1, 1], [11, 4, 3, 2], [11, 4, 4, 1], [11, 5, 1, 1, 1, 1], 
[11, 5, 2, 1, 1], [11, 5, 2, 2], [11, 5, 3, 1], [11, 5, 4], [11, 6, 1, 1, 1], 
[11, 6, 2, 1], [11, 6, 3], [11, 7, 1, 1], [11, 7, 2], [11, 8, 1], [11, 9], 
[12, 1, 1, 1, 1, 1, 1, 1, 1], [12, 2, 1, 1, 1, 1, 1, 1], 
[12, 2, 2, 1, 1, 1, 1], [12, 2, 2, 2, 1, 1], [12, 2, 2, 2, 2], 
[12, 3, 1, 1, 1, 1, 1], [12, 3, 2, 1, 1, 1], [12, 3, 2, 2, 1], 
[12, 3, 3, 1, 1], [12, 3, 3, 2], [12, 4, 1, 1, 1, 1], [12, 4, 2, 1, 1], 
[12, 4, 2, 2], [12, 4, 3, 1], [12, 4, 4], [12, 5, 1, 1, 1], [12, 5, 2, 1], 
[12, 5, 3], [12, 6, 1, 1], [12, 6, 2], [12, 7, 1], [12, 8], 
[13, 1, 1, 1, 1, 1, 1, 1], [13, 2, 1, 1, 1, 1, 1], [13, 2, 2, 1, 1, 1], 
[13, 2, 2, 2, 1], [13, 3, 1, 1, 1, 1], [13, 3, 2, 1, 1], [13, 3, 2, 2], 
[13, 3, 3, 1], [13, 4, 1, 1, 1], [13, 4, 2, 1], [13, 4, 3], [13, 5, 1, 1], 
[13, 5, 2], [13, 6, 1], [13, 7], [14, 1, 1, 1, 1, 1, 1], [14, 2, 1, 1, 1, 1], 
[14, 2, 2, 1, 1], [14, 2, 2, 2], [14, 3, 1, 1, 1], [14, 3, 2, 1], [14, 3, 3], 
[14, 4, 1, 1], [14, 4, 2], [14, 5, 1], [14, 6], [15, 1, 1, 1, 1, 1], 
[15, 2, 1, 1, 1], [15, 2, 2, 1], [15, 3, 1, 1], [15, 3, 2], [15, 4, 1], 
[15, 5], [16, 1, 1, 1, 1], [16, 2, 1, 1], [16, 2, 2], [16, 3, 1], [16, 4], 
[17, 1, 1, 1], [17, 2, 1], [17, 3], [18, 1, 1], [18, 2], [19, 1], [20]}
(%i2)  s: integer_partitions (4);
(%o2)           {[1, 1, 1, 1], [2, 1, 1], [2, 2], [3, 1], [4]}
(%i3)  cardinality (s);
(%o3)                                  5
(%i4)  map (lambda ([x], apply ("+", x)), s);
(%o4)                                 {4}
(%i5)  integer_partitions (20, 4);
(%o5) {[5, 5, 5, 5], [6, 5, 5, 4], [6, 6, 4, 4], [6, 6, 5, 3], [6, 6, 6, 2], 
[7, 5, 4, 4], [7, 5, 5, 3], [7, 6, 4, 3], [7, 6, 5, 2], [7, 6, 6, 1], 
[7, 7, 3, 3], [7, 7, 4, 2], [7, 7, 5, 1], [7, 7, 6, 0], [8, 4, 4, 4], 
[8, 5, 4, 3], [8, 5, 5, 2], [8, 6, 3, 3], [8, 6, 4, 2], [8, 6, 5, 1], 
[8, 6, 6, 0], [8, 7, 3, 2], [8, 7, 4, 1], [8, 7, 5, 0], [8, 8, 2, 2], 
[8, 8, 3, 1], [8, 8, 4, 0], [9, 4, 4, 3], [9, 5, 3, 3], [9, 5, 4, 2], 
[9, 5, 5, 1], [9, 6, 3, 2], [9, 6, 4, 1], [9, 6, 5, 0], [9, 7, 2, 2], 
[9, 7, 3, 1], [9, 7, 4, 0], [9, 8, 2, 1], [9, 8, 3, 0], [9, 9, 1, 1], 
[9, 9, 2, 0], [10, 4, 3, 3], [10, 4, 4, 2], [10, 5, 3, 2], [10, 5, 4, 1], 
[10, 5, 5, 0], [10, 6, 2, 2], [10, 6, 3, 1], [10, 6, 4, 0], [10, 7, 2, 1], 
[10, 7, 3, 0], [10, 8, 1, 1], [10, 8, 2, 0], [10, 9, 1, 0], [10, 10, 0, 0], 
[11, 3, 3, 3], [11, 4, 3, 2], [11, 4, 4, 1], [11, 5, 2, 2], [11, 5, 3, 1], 
[11, 5, 4, 0], [11, 6, 2, 1], [11, 6, 3, 0], [11, 7, 1, 1], [11, 7, 2, 0], 
[11, 8, 1, 0], [11, 9, 0, 0], [12, 3, 3, 2], [12, 4, 2, 2], [12, 4, 3, 1], 
[12, 4, 4, 0], [12, 5, 2, 1], [12, 5, 3, 0], [12, 6, 1, 1], [12, 6, 2, 0], 
[12, 7, 1, 0], [12, 8, 0, 0], [13, 3, 2, 2], [13, 3, 3, 1], [13, 4, 2, 1], 
[13, 4, 3, 0], [13, 5, 1, 1], [13, 5, 2, 0], [13, 6, 1, 0], [13, 7, 0, 0], 
[14, 2, 2, 2], [14, 3, 2, 1], [14, 3, 3, 0], [14, 4, 1, 1], [14, 4, 2, 0], 
[14, 5, 1, 0], [14, 6, 0, 0], [15, 2, 2, 1], [15, 3, 1, 1], [15, 3, 2, 0], 
[15, 4, 1, 0], [15, 5, 0, 0], [16, 2, 1, 1], [16, 2, 2, 0], [16, 3, 1, 0], 
[16, 4, 0, 0], [17, 1, 1, 1], [17, 2, 1, 0], [17, 3, 0, 0], [18, 1, 1, 0], 
[18, 2, 0, 0], [19, 1, 0, 0], [20, 0, 0, 0]}
(%i6)  integer_partitions (20, 4);
(%o6) {[5, 5, 5, 5], [6, 5, 5, 4], [6, 6, 4, 4], [6, 6, 5, 3], [6, 6, 6, 2], 
[7, 5, 4, 4], [7, 5, 5, 3], [7, 6, 4, 3], [7, 6, 5, 2], [7, 6, 6, 1], 
[7, 7, 3, 3], [7, 7, 4, 2], [7, 7, 5, 1], [7, 7, 6, 0], [8, 4, 4, 4], 
[8, 5, 4, 3], [8, 5, 5, 2], [8, 6, 3, 3], [8, 6, 4, 2], [8, 6, 5, 1], 
[8, 6, 6, 0], [8, 7, 3, 2], [8, 7, 4, 1], [8, 7, 5, 0], [8, 8, 2, 2], 
[8, 8, 3, 1], [8, 8, 4, 0], [9, 4, 4, 3], [9, 5, 3, 3], [9, 5, 4, 2], 
[9, 5, 5, 1], [9, 6, 3, 2], [9, 6, 4, 1], [9, 6, 5, 0], [9, 7, 2, 2], 
[9, 7, 3, 1], [9, 7, 4, 0], [9, 8, 2, 1], [9, 8, 3, 0], [9, 9, 1, 1], 
[9, 9, 2, 0], [10, 4, 3, 3], [10, 4, 4, 2], [10, 5, 3, 2], [10, 5, 4, 1], 
[10, 5, 5, 0], [10, 6, 2, 2], [10, 6, 3, 1], [10, 6, 4, 0], [10, 7, 2, 1], 
[10, 7, 3, 0], [10, 8, 1, 1], [10, 8, 2, 0], [10, 9, 1, 0], [10, 10, 0, 0], 
[11, 3, 3, 3], [11, 4, 3, 2], [11, 4, 4, 1], [11, 5, 2, 2], [11, 5, 3, 1], 
[11, 5, 4, 0], [11, 6, 2, 1], [11, 6, 3, 0], [11, 7, 1, 1], [11, 7, 2, 0], 
[11, 8, 1, 0], [11, 9, 0, 0], [12, 3, 3, 2], [12, 4, 2, 2], [12, 4, 3, 1], 
[12, 4, 4, 0], [12, 5, 2, 1], [12, 5, 3, 0], [12, 6, 1, 1], [12, 6, 2, 0], 
[12, 7, 1, 0], [12, 8, 0, 0], [13, 3, 2, 2], [13, 3, 3, 1], [13, 4, 2, 1], 
[13, 4, 3, 0], [13, 5, 1, 1], [13, 5, 2, 0], [13, 6, 1, 0], [13, 7, 0, 0], 
[14, 2, 2, 2], [14, 3, 2, 1], [14, 3, 3, 0], [14, 4, 1, 1], [14, 4, 2, 0], 
[14, 5, 1, 0], [14, 6, 0, 0], [15, 2, 2, 1], [15, 3, 1, 1], [15, 3, 2, 0], 
[15, 4, 1, 0], [15, 5, 0, 0], [16, 2, 1, 1], [16, 2, 2, 0], [16, 3, 1, 0], 
[16, 4, 0, 0], [17, 1, 1, 1], [17, 2, 1, 0], [17, 3, 0, 0], [18, 1, 1, 0], 
[18, 2, 0, 0], [19, 1, 0, 0], [20, 0, 0, 0]}
(%i7)  s: integer_partitions (20, 4);
(%o7) {[5, 5, 5, 5], [6, 5, 5, 4], [6, 6, 4, 4], [6, 6, 5, 3], [6, 6, 6, 2], 
[7, 5, 4, 4], [7, 5, 5, 3], [7, 6, 4, 3], [7, 6, 5, 2], [7, 6, 6, 1], 
[7, 7, 3, 3], [7, 7, 4, 2], [7, 7, 5, 1], [7, 7, 6, 0], [8, 4, 4, 4], 
[8, 5, 4, 3], [8, 5, 5, 2], [8, 6, 3, 3], [8, 6, 4, 2], [8, 6, 5, 1], 
[8, 6, 6, 0], [8, 7, 3, 2], [8, 7, 4, 1], [8, 7, 5, 0], [8, 8, 2, 2], 
[8, 8, 3, 1], [8, 8, 4, 0], [9, 4, 4, 3], [9, 5, 3, 3], [9, 5, 4, 2], 
[9, 5, 5, 1], [9, 6, 3, 2], [9, 6, 4, 1], [9, 6, 5, 0], [9, 7, 2, 2], 
[9, 7, 3, 1], [9, 7, 4, 0], [9, 8, 2, 1], [9, 8, 3, 0], [9, 9, 1, 1], 
[9, 9, 2, 0], [10, 4, 3, 3], [10, 4, 4, 2], [10, 5, 3, 2], [10, 5, 4, 1], 
[10, 5, 5, 0], [10, 6, 2, 2], [10, 6, 3, 1], [10, 6, 4, 0], [10, 7, 2, 1], 
[10, 7, 3, 0], [10, 8, 1, 1], [10, 8, 2, 0], [10, 9, 1, 0], [10, 10, 0, 0], 
[11, 3, 3, 3], [11, 4, 3, 2], [11, 4, 4, 1], [11, 5, 2, 2], [11, 5, 3, 1], 
[11, 5, 4, 0], [11, 6, 2, 1], [11, 6, 3, 0], [11, 7, 1, 1], [11, 7, 2, 0], 
[11, 8, 1, 0], [11, 9, 0, 0], [12, 3, 3, 2], [12, 4, 2, 2], [12, 4, 3, 1], 
[12, 4, 4, 0], [12, 5, 2, 1], [12, 5, 3, 0], [12, 6, 1, 1], [12, 6, 2, 0], 
[12, 7, 1, 0], [12, 8, 0, 0], [13, 3, 2, 2], [13, 3, 3, 1], [13, 4, 2, 1], 
[13, 4, 3, 0], [13, 5, 1, 1], [13, 5, 2, 0], [13, 6, 1, 0], [13, 7, 0, 0], 
[14, 2, 2, 2], [14, 3, 2, 1], [14, 3, 3, 0], [14, 4, 1, 1], [14, 4, 2, 0], 
[14, 5, 1, 0], [14, 6, 0, 0], [15, 2, 2, 1], [15, 3, 1, 1], [15, 3, 2, 0], 
[15, 4, 1, 0], [15, 5, 0, 0], [16, 2, 1, 1], [16, 2, 2, 0], [16, 3, 1, 0], 
[16, 4, 0, 0], [17, 1, 1, 1], [17, 2, 1, 0], [17, 3, 0, 0], [18, 1, 1, 0], 
[18, 2, 0, 0], [19, 1, 0, 0], [20, 0, 0, 0]}
(%i8)  cardinality (s);
(%o8)                                 108
(%i9)  xprimep(x) := integerp(x) and (x >
 1) and primep(x);
(%o9)         xprimep(x) := integerp(x) and (x > 1) and primep(x)
(%i10)  subset (s, lambda ([x], every (xprimep, x)));
(%o10) {[5, 5, 5, 5], [7, 5, 5, 3], [7, 7, 3, 3], [11, 3, 3, 3], 
                                                  [11, 5, 2, 2], [13, 3, 2, 2]}
(%i11) 
Run Example
integer_partitions (4);
(%o1)           {[1, 1, 1, 1], [2, 1, 1], [2, 2], [3, 1], [4]}
(%i2)  s: integer_partitions (20);
(%o2) {[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], 
[2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1], 
[2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 
[3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1], 
[3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1], [3, 2, 2, 2, 2, 2, 2, 2, 2, 1], 
[3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1], 
[3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1], [3, 3, 2, 2, 2, 2, 2, 2, 1, 1], 
[3, 3, 2, 2, 2, 2, 2, 2, 2], [3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1], 
[3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1], [3, 3, 3, 2, 2, 2, 2, 1, 1, 1], 
[3, 3, 3, 2, 2, 2, 2, 2, 1], [3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1], 
[3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1], [3, 3, 3, 3, 2, 2, 1, 1, 1, 1], 
[3, 3, 3, 3, 2, 2, 2, 1, 1], [3, 3, 3, 3, 2, 2, 2, 2], 
[3, 3, 3, 3, 3, 1, 1, 1, 1, 1], [3, 3, 3, 3, 3, 2, 1, 1, 1], 
[3, 3, 3, 3, 3, 2, 2, 1], [3, 3, 3, 3, 3, 3, 1, 1], [3, 3, 3, 3, 3, 3, 2], 
[4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [4, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1], 
[4, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1], [4, 2, 2, 2, 2, 2, 2, 2, 1, 1], 
[4, 2, 2, 2, 2, 2, 2, 2, 2], [4, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], 
[4, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1], [4, 3, 2, 2, 2, 2, 2, 1, 1, 1], 
[4, 3, 2, 2, 2, 2, 2, 2, 1], [4, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1], [4, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1], 
[4, 3, 3, 2, 2, 2, 1, 1, 1, 1], [4, 3, 3, 2, 2, 2, 2, 1, 1], 
[4, 3, 3, 2, 2, 2, 2, 2], [4, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1], 
[4, 3, 3, 3, 2, 1, 1, 1, 1, 1], [4, 3, 3, 3, 2, 2, 1, 1, 1], 
[4, 3, 3, 3, 2, 2, 2, 1], [4, 3, 3, 3, 3, 1, 1, 1, 1], 
[4, 3, 3, 3, 3, 2, 1, 1], [4, 3, 3, 3, 3, 2, 2], [4, 3, 3, 3, 3, 3, 1], 
[4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], 
[4, 4, 2, 2, 2, 1, 1, 1, 1, 1, 1], [4, 4, 2, 2, 2, 2, 1, 1, 1, 1], 
[4, 4, 2, 2, 2, 2, 2, 1, 1], [4, 4, 2, 2, 2, 2, 2, 2], 
[4, 4, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1], 
[4, 4, 3, 2, 2, 1, 1, 1, 1, 1], [4, 4, 3, 2, 2, 2, 1, 1, 1], 
[4, 4, 3, 2, 2, 2, 2, 1], [4, 4, 3, 3, 1, 1, 1, 1, 1, 1], 
[4, 4, 3, 3, 2, 1, 1, 1, 1], [4, 4, 3, 3, 2, 2, 1, 1], [4, 4, 3, 3, 2, 2, 2], 
[4, 4, 3, 3, 3, 1, 1, 1], [4, 4, 3, 3, 3, 2, 1], [4, 4, 3, 3, 3, 3], 
[4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 2, 1, 1, 1, 1, 1, 1], 
[4, 4, 4, 2, 2, 1, 1, 1, 1], [4, 4, 4, 2, 2, 2, 1, 1], [4, 4, 4, 2, 2, 2, 2], 
[4, 4, 4, 3, 1, 1, 1, 1, 1], [4, 4, 4, 3, 2, 1, 1, 1], [4, 4, 4, 3, 2, 2, 1], 
[4, 4, 4, 3, 3, 1, 1], [4, 4, 4, 3, 3, 2], [4, 4, 4, 4, 1, 1, 1, 1], 
[4, 4, 4, 4, 2, 1, 1], [4, 4, 4, 4, 2, 2], [4, 4, 4, 4, 3, 1], 
[4, 4, 4, 4, 4], [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[5, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[5, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[5, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], 
[5, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1], [5, 2, 2, 2, 2, 2, 2, 1, 1, 1], 
[5, 2, 2, 2, 2, 2, 2, 2, 1], [5, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[5, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], 
[5, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1], [5, 3, 2, 2, 2, 2, 1, 1, 1, 1], 
[5, 3, 2, 2, 2, 2, 2, 1, 1], [5, 3, 2, 2, 2, 2, 2, 2], 
[5, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1], 
[5, 3, 3, 2, 2, 1, 1, 1, 1, 1], [5, 3, 3, 2, 2, 2, 1, 1, 1], 
[5, 3, 3, 2, 2, 2, 2, 1], [5, 3, 3, 3, 1, 1, 1, 1, 1, 1], 
[5, 3, 3, 3, 2, 1, 1, 1, 1], [5, 3, 3, 3, 2, 2, 1, 1], [5, 3, 3, 3, 2, 2, 2], 
[5, 3, 3, 3, 3, 1, 1, 1], [5, 3, 3, 3, 3, 2, 1], [5, 3, 3, 3, 3, 3], 
[5, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[5, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1], [5, 4, 2, 2, 2, 1, 1, 1, 1, 1], 
[5, 4, 2, 2, 2, 2, 1, 1, 1], [5, 4, 2, 2, 2, 2, 2, 1], 
[5, 4, 3, 1, 1, 1, 1, 1, 1, 1, 1], [5, 4, 3, 2, 1, 1, 1, 1, 1, 1], 
[5, 4, 3, 2, 2, 1, 1, 1, 1], [5, 4, 3, 2, 2, 2, 1, 1], [5, 4, 3, 2, 2, 2, 2], 
[5, 4, 3, 3, 1, 1, 1, 1, 1], [5, 4, 3, 3, 2, 1, 1, 1], [5, 4, 3, 3, 2, 2, 1], 
[5, 4, 3, 3, 3, 1, 1], [5, 4, 3, 3, 3, 2], [5, 4, 4, 1, 1, 1, 1, 1, 1, 1], 
[5, 4, 4, 2, 1, 1, 1, 1, 1], [5, 4, 4, 2, 2, 1, 1, 1], [5, 4, 4, 2, 2, 2, 1], 
[5, 4, 4, 3, 1, 1, 1, 1], [5, 4, 4, 3, 2, 1, 1], [5, 4, 4, 3, 2, 2], 
[5, 4, 4, 3, 3, 1], [5, 4, 4, 4, 1, 1, 1], [5, 4, 4, 4, 2, 1], 
[5, 4, 4, 4, 3], [5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[5, 5, 2, 1, 1, 1, 1, 1, 1, 1, 1], [5, 5, 2, 2, 1, 1, 1, 1, 1, 1], 
[5, 5, 2, 2, 2, 1, 1, 1, 1], [5, 5, 2, 2, 2, 2, 1, 1], [5, 5, 2, 2, 2, 2, 2], 
[5, 5, 3, 1, 1, 1, 1, 1, 1, 1], [5, 5, 3, 2, 1, 1, 1, 1, 1], 
[5, 5, 3, 2, 2, 1, 1, 1], [5, 5, 3, 2, 2, 2, 1], [5, 5, 3, 3, 1, 1, 1, 1], 
[5, 5, 3, 3, 2, 1, 1], [5, 5, 3, 3, 2, 2], [5, 5, 3, 3, 3, 1], 
[5, 5, 4, 1, 1, 1, 1, 1, 1], [5, 5, 4, 2, 1, 1, 1, 1], [5, 5, 4, 2, 2, 1, 1], 
[5, 5, 4, 2, 2, 2], [5, 5, 4, 3, 1, 1, 1], [5, 5, 4, 3, 2, 1], 
[5, 5, 4, 3, 3], [5, 5, 4, 4, 1, 1], [5, 5, 4, 4, 2], 
[5, 5, 5, 1, 1, 1, 1, 1], [5, 5, 5, 2, 1, 1, 1], [5, 5, 5, 2, 2, 1], 
[5, 5, 5, 3, 1, 1], [5, 5, 5, 3, 2], [5, 5, 5, 4, 1], [5, 5, 5, 5], 
[6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[6, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[6, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [6, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], 
[6, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1], [6, 2, 2, 2, 2, 2, 1, 1, 1, 1], 
[6, 2, 2, 2, 2, 2, 2, 1, 1], [6, 2, 2, 2, 2, 2, 2, 2], 
[6, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [6, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[6, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1], [6, 3, 2, 2, 2, 1, 1, 1, 1, 1], 
[6, 3, 2, 2, 2, 2, 1, 1, 1], [6, 3, 2, 2, 2, 2, 2, 1], 
[6, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1], [6, 3, 3, 2, 1, 1, 1, 1, 1, 1], 
[6, 3, 3, 2, 2, 1, 1, 1, 1], [6, 3, 3, 2, 2, 2, 1, 1], [6, 3, 3, 2, 2, 2, 2], 
[6, 3, 3, 3, 1, 1, 1, 1, 1], [6, 3, 3, 3, 2, 1, 1, 1], [6, 3, 3, 3, 2, 2, 1], 
[6, 3, 3, 3, 3, 1, 1], [6, 3, 3, 3, 3, 2], 
[6, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [6, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1], 
[6, 4, 2, 2, 1, 1, 1, 1, 1, 1], [6, 4, 2, 2, 2, 1, 1, 1, 1], 
[6, 4, 2, 2, 2, 2, 1, 1], [6, 4, 2, 2, 2, 2, 2], 
[6, 4, 3, 1, 1, 1, 1, 1, 1, 1], [6, 4, 3, 2, 1, 1, 1, 1, 1], 
[6, 4, 3, 2, 2, 1, 1, 1], [6, 4, 3, 2, 2, 2, 1], [6, 4, 3, 3, 1, 1, 1, 1], 
[6, 4, 3, 3, 2, 1, 1], [6, 4, 3, 3, 2, 2], [6, 4, 3, 3, 3, 1], 
[6, 4, 4, 1, 1, 1, 1, 1, 1], [6, 4, 4, 2, 1, 1, 1, 1], [6, 4, 4, 2, 2, 1, 1], 
[6, 4, 4, 2, 2, 2], [6, 4, 4, 3, 1, 1, 1], [6, 4, 4, 3, 2, 1], 
[6, 4, 4, 3, 3], [6, 4, 4, 4, 1, 1], [6, 4, 4, 4, 2], 
[6, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1], [6, 5, 2, 1, 1, 1, 1, 1, 1, 1], 
[6, 5, 2, 2, 1, 1, 1, 1, 1], [6, 5, 2, 2, 2, 1, 1, 1], [6, 5, 2, 2, 2, 2, 1], 
[6, 5, 3, 1, 1, 1, 1, 1, 1], [6, 5, 3, 2, 1, 1, 1, 1], [6, 5, 3, 2, 2, 1, 1], 
[6, 5, 3, 2, 2, 2], [6, 5, 3, 3, 1, 1, 1], [6, 5, 3, 3, 2, 1], 
[6, 5, 3, 3, 3], [6, 5, 4, 1, 1, 1, 1, 1], [6, 5, 4, 2, 1, 1, 1], 
[6, 5, 4, 2, 2, 1], [6, 5, 4, 3, 1, 1], [6, 5, 4, 3, 2], [6, 5, 4, 4, 1], 
[6, 5, 5, 1, 1, 1, 1], [6, 5, 5, 2, 1, 1], [6, 5, 5, 2, 2], [6, 5, 5, 3, 1], 
[6, 5, 5, 4], [6, 6, 1, 1, 1, 1, 1, 1, 1, 1], [6, 6, 2, 1, 1, 1, 1, 1, 1], 
[6, 6, 2, 2, 1, 1, 1, 1], [6, 6, 2, 2, 2, 1, 1], [6, 6, 2, 2, 2, 2], 
[6, 6, 3, 1, 1, 1, 1, 1], [6, 6, 3, 2, 1, 1, 1], [6, 6, 3, 2, 2, 1], 
[6, 6, 3, 3, 1, 1], [6, 6, 3, 3, 2], [6, 6, 4, 1, 1, 1, 1], 
[6, 6, 4, 2, 1, 1], [6, 6, 4, 2, 2], [6, 6, 4, 3, 1], [6, 6, 4, 4], 
[6, 6, 5, 1, 1, 1], [6, 6, 5, 2, 1], [6, 6, 5, 3], [6, 6, 6, 1, 1], 
[6, 6, 6, 2], [7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[7, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[7, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [7, 2, 2, 2, 2, 1, 1, 1, 1, 1], 
[7, 2, 2, 2, 2, 2, 1, 1, 1], [7, 2, 2, 2, 2, 2, 2, 1], 
[7, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1], 
[7, 3, 2, 2, 1, 1, 1, 1, 1, 1], [7, 3, 2, 2, 2, 1, 1, 1, 1], 
[7, 3, 2, 2, 2, 2, 1, 1], [7, 3, 2, 2, 2, 2, 2], 
[7, 3, 3, 1, 1, 1, 1, 1, 1, 1], [7, 3, 3, 2, 1, 1, 1, 1, 1], 
[7, 3, 3, 2, 2, 1, 1, 1], [7, 3, 3, 2, 2, 2, 1], [7, 3, 3, 3, 1, 1, 1, 1], 
[7, 3, 3, 3, 2, 1, 1], [7, 3, 3, 3, 2, 2], [7, 3, 3, 3, 3, 1], 
[7, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1], [7, 4, 2, 1, 1, 1, 1, 1, 1, 1], 
[7, 4, 2, 2, 1, 1, 1, 1, 1], [7, 4, 2, 2, 2, 1, 1, 1], [7, 4, 2, 2, 2, 2, 1], 
[7, 4, 3, 1, 1, 1, 1, 1, 1], [7, 4, 3, 2, 1, 1, 1, 1], [7, 4, 3, 2, 2, 1, 1], 
[7, 4, 3, 2, 2, 2], [7, 4, 3, 3, 1, 1, 1], [7, 4, 3, 3, 2, 1], 
[7, 4, 3, 3, 3], [7, 4, 4, 1, 1, 1, 1, 1], [7, 4, 4, 2, 1, 1, 1], 
[7, 4, 4, 2, 2, 1], [7, 4, 4, 3, 1, 1], [7, 4, 4, 3, 2], [7, 4, 4, 4, 1], 
[7, 5, 1, 1, 1, 1, 1, 1, 1, 1], [7, 5, 2, 1, 1, 1, 1, 1, 1], 
[7, 5, 2, 2, 1, 1, 1, 1], [7, 5, 2, 2, 2, 1, 1], [7, 5, 2, 2, 2, 2], 
[7, 5, 3, 1, 1, 1, 1, 1], [7, 5, 3, 2, 1, 1, 1], [7, 5, 3, 2, 2, 1], 
[7, 5, 3, 3, 1, 1], [7, 5, 3, 3, 2], [7, 5, 4, 1, 1, 1, 1], 
[7, 5, 4, 2, 1, 1], [7, 5, 4, 2, 2], [7, 5, 4, 3, 1], [7, 5, 4, 4], 
[7, 5, 5, 1, 1, 1], [7, 5, 5, 2, 1], [7, 5, 5, 3], 
[7, 6, 1, 1, 1, 1, 1, 1, 1], [7, 6, 2, 1, 1, 1, 1, 1], [7, 6, 2, 2, 1, 1, 1], 
[7, 6, 2, 2, 2, 1], [7, 6, 3, 1, 1, 1, 1], [7, 6, 3, 2, 1, 1], 
[7, 6, 3, 2, 2], [7, 6, 3, 3, 1], [7, 6, 4, 1, 1, 1], [7, 6, 4, 2, 1], 
[7, 6, 4, 3], [7, 6, 5, 1, 1], [7, 6, 5, 2], [7, 6, 6, 1], 
[7, 7, 1, 1, 1, 1, 1, 1], [7, 7, 2, 1, 1, 1, 1], [7, 7, 2, 2, 1, 1], 
[7, 7, 2, 2, 2], [7, 7, 3, 1, 1, 1], [7, 7, 3, 2, 1], [7, 7, 3, 3], 
[7, 7, 4, 1, 1], [7, 7, 4, 2], [7, 7, 5, 1], [7, 7, 6], 
[8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[8, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [8, 2, 2, 2, 1, 1, 1, 1, 1, 1], 
[8, 2, 2, 2, 2, 1, 1, 1, 1], [8, 2, 2, 2, 2, 2, 1, 1], [8, 2, 2, 2, 2, 2, 2], 
[8, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 3, 2, 1, 1, 1, 1, 1, 1, 1], 
[8, 3, 2, 2, 1, 1, 1, 1, 1], [8, 3, 2, 2, 2, 1, 1, 1], [8, 3, 2, 2, 2, 2, 1], 
[8, 3, 3, 1, 1, 1, 1, 1, 1], [8, 3, 3, 2, 1, 1, 1, 1], [8, 3, 3, 2, 2, 1, 1], 
[8, 3, 3, 2, 2, 2], [8, 3, 3, 3, 1, 1, 1], [8, 3, 3, 3, 2, 1], 
[8, 3, 3, 3, 3], [8, 4, 1, 1, 1, 1, 1, 1, 1, 1], [8, 4, 2, 1, 1, 1, 1, 1, 1], 
[8, 4, 2, 2, 1, 1, 1, 1], [8, 4, 2, 2, 2, 1, 1], [8, 4, 2, 2, 2, 2], 
[8, 4, 3, 1, 1, 1, 1, 1], [8, 4, 3, 2, 1, 1, 1], [8, 4, 3, 2, 2, 1], 
[8, 4, 3, 3, 1, 1], [8, 4, 3, 3, 2], [8, 4, 4, 1, 1, 1, 1], 
[8, 4, 4, 2, 1, 1], [8, 4, 4, 2, 2], [8, 4, 4, 3, 1], [8, 4, 4, 4], 
[8, 5, 1, 1, 1, 1, 1, 1, 1], [8, 5, 2, 1, 1, 1, 1, 1], [8, 5, 2, 2, 1, 1, 1], 
[8, 5, 2, 2, 2, 1], [8, 5, 3, 1, 1, 1, 1], [8, 5, 3, 2, 1, 1], 
[8, 5, 3, 2, 2], [8, 5, 3, 3, 1], [8, 5, 4, 1, 1, 1], [8, 5, 4, 2, 1], 
[8, 5, 4, 3], [8, 5, 5, 1, 1], [8, 5, 5, 2], [8, 6, 1, 1, 1, 1, 1, 1], 
[8, 6, 2, 1, 1, 1, 1], [8, 6, 2, 2, 1, 1], [8, 6, 2, 2, 2], 
[8, 6, 3, 1, 1, 1], [8, 6, 3, 2, 1], [8, 6, 3, 3], [8, 6, 4, 1, 1], 
[8, 6, 4, 2], [8, 6, 5, 1], [8, 6, 6], [8, 7, 1, 1, 1, 1, 1], 
[8, 7, 2, 1, 1, 1], [8, 7, 2, 2, 1], [8, 7, 3, 1, 1], [8, 7, 3, 2], 
[8, 7, 4, 1], [8, 7, 5], [8, 8, 1, 1, 1, 1], [8, 8, 2, 1, 1], [8, 8, 2, 2], 
[8, 8, 3, 1], [8, 8, 4], [9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
[9, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [9, 2, 2, 1, 1, 1, 1, 1, 1, 1], 
[9, 2, 2, 2, 1, 1, 1, 1, 1], [9, 2, 2, 2, 2, 1, 1, 1], [9, 2, 2, 2, 2, 2, 1], 
[9, 3, 1, 1, 1, 1, 1, 1, 1, 1], [9, 3, 2, 1, 1, 1, 1, 1, 1], 
[9, 3, 2, 2, 1, 1, 1, 1], [9, 3, 2, 2, 2, 1, 1], [9, 3, 2, 2, 2, 2], 
[9, 3, 3, 1, 1, 1, 1, 1], [9, 3, 3, 2, 1, 1, 1], [9, 3, 3, 2, 2, 1], 
[9, 3, 3, 3, 1, 1], [9, 3, 3, 3, 2], [9, 4, 1, 1, 1, 1, 1, 1, 1], 
[9, 4, 2, 1, 1, 1, 1, 1], [9, 4, 2, 2, 1, 1, 1], [9, 4, 2, 2, 2, 1], 
[9, 4, 3, 1, 1, 1, 1], [9, 4, 3, 2, 1, 1], [9, 4, 3, 2, 2], [9, 4, 3, 3, 1], 
[9, 4, 4, 1, 1, 1], [9, 4, 4, 2, 1], [9, 4, 4, 3], [9, 5, 1, 1, 1, 1, 1, 1], 
[9, 5, 2, 1, 1, 1, 1], [9, 5, 2, 2, 1, 1], [9, 5, 2, 2, 2], 
[9, 5, 3, 1, 1, 1], [9, 5, 3, 2, 1], [9, 5, 3, 3], [9, 5, 4, 1, 1], 
[9, 5, 4, 2], [9, 5, 5, 1], [9, 6, 1, 1, 1, 1, 1], [9, 6, 2, 1, 1, 1], 
[9, 6, 2, 2, 1], [9, 6, 3, 1, 1], [9, 6, 3, 2], [9, 6, 4, 1], [9, 6, 5], 
[9, 7, 1, 1, 1, 1], [9, 7, 2, 1, 1], [9, 7, 2, 2], [9, 7, 3, 1], [9, 7, 4], 
[9, 8, 1, 1, 1], [9, 8, 2, 1], [9, 8, 3], [9, 9, 1, 1], [9, 9, 2], 
[10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [10, 2, 1, 1, 1, 1, 1, 1, 1, 1], 
[10, 2, 2, 1, 1, 1, 1, 1, 1], [10, 2, 2, 2, 1, 1, 1, 1], 
[10, 2, 2, 2, 2, 1, 1], [10, 2, 2, 2, 2, 2], [10, 3, 1, 1, 1, 1, 1, 1, 1], 
[10, 3, 2, 1, 1, 1, 1, 1], [10, 3, 2, 2, 1, 1, 1], [10, 3, 2, 2, 2, 1], 
[10, 3, 3, 1, 1, 1, 1], [10, 3, 3, 2, 1, 1], [10, 3, 3, 2, 2], 
[10, 3, 3, 3, 1], [10, 4, 1, 1, 1, 1, 1, 1], [10, 4, 2, 1, 1, 1, 1], 
[10, 4, 2, 2, 1, 1], [10, 4, 2, 2, 2], [10, 4, 3, 1, 1, 1], [10, 4, 3, 2, 1], 
[10, 4, 3, 3], [10, 4, 4, 1, 1], [10, 4, 4, 2], [10, 5, 1, 1, 1, 1, 1], 
[10, 5, 2, 1, 1, 1], [10, 5, 2, 2, 1], [10, 5, 3, 1, 1], [10, 5, 3, 2], 
[10, 5, 4, 1], [10, 5, 5], [10, 6, 1, 1, 1, 1], [10, 6, 2, 1, 1], 
[10, 6, 2, 2], [10, 6, 3, 1], [10, 6, 4], [10, 7, 1, 1, 1], [10, 7, 2, 1], 
[10, 7, 3], [10, 8, 1, 1], [10, 8, 2], [10, 9, 1], [10, 10], 
[11, 1, 1, 1, 1, 1, 1, 1, 1, 1], [11, 2, 1, 1, 1, 1, 1, 1, 1], 
[11, 2, 2, 1, 1, 1, 1, 1], [11, 2, 2, 2, 1, 1, 1], [11, 2, 2, 2, 2, 1], 
[11, 3, 1, 1, 1, 1, 1, 1], [11, 3, 2, 1, 1, 1, 1], [11, 3, 2, 2, 1, 1], 
[11, 3, 2, 2, 2], [11, 3, 3, 1, 1, 1], [11, 3, 3, 2, 1], [11, 3, 3, 3], 
[11, 4, 1, 1, 1, 1, 1], [11, 4, 2, 1, 1, 1], [11, 4, 2, 2, 1], 
[11, 4, 3, 1, 1], [11, 4, 3, 2], [11, 4, 4, 1], [11, 5, 1, 1, 1, 1], 
[11, 5, 2, 1, 1], [11, 5, 2, 2], [11, 5, 3, 1], [11, 5, 4], [11, 6, 1, 1, 1], 
[11, 6, 2, 1], [11, 6, 3], [11, 7, 1, 1], [11, 7, 2], [11, 8, 1], [11, 9], 
[12, 1, 1, 1, 1, 1, 1, 1, 1], [12, 2, 1, 1, 1, 1, 1, 1], 
[12, 2, 2, 1, 1, 1, 1], [12, 2, 2, 2, 1, 1], [12, 2, 2, 2, 2], 
[12, 3, 1, 1, 1, 1, 1], [12, 3, 2, 1, 1, 1], [12, 3, 2, 2, 1], 
[12, 3, 3, 1, 1], [12, 3, 3, 2], [12, 4, 1, 1, 1, 1], [12, 4, 2, 1, 1], 
[12, 4, 2, 2], [12, 4, 3, 1], [12, 4, 4], [12, 5, 1, 1, 1], [12, 5, 2, 1], 
[12, 5, 3], [12, 6, 1, 1], [12, 6, 2], [12, 7, 1], [12, 8], 
[13, 1, 1, 1, 1, 1, 1, 1], [13, 2, 1, 1, 1, 1, 1], [13, 2, 2, 1, 1, 1], 
[13, 2, 2, 2, 1], [13, 3, 1, 1, 1, 1], [13, 3, 2, 1, 1], [13, 3, 2, 2], 
[13, 3, 3, 1], [13, 4, 1, 1, 1], [13, 4, 2, 1], [13, 4, 3], [13, 5, 1, 1], 
[13, 5, 2], [13, 6, 1], [13, 7], [14, 1, 1, 1, 1, 1, 1], [14, 2, 1, 1, 1, 1], 
[14, 2, 2, 1, 1], [14, 2, 2, 2], [14, 3, 1, 1, 1], [14, 3, 2, 1], [14, 3, 3], 
[14, 4, 1, 1], [14, 4, 2], [14, 5, 1], [14, 6], [15, 1, 1, 1, 1, 1], 
[15, 2, 1, 1, 1], [15, 2, 2, 1], [15, 3, 1, 1], [15, 3, 2], [15, 4, 1], 
[15, 5], [16, 1, 1, 1, 1], [16, 2, 1, 1], [16, 2, 2], [16, 3, 1], [16, 4], 
[17, 1, 1, 1], [17, 2, 1], [17, 3], [18, 1, 1], [18, 2], [19, 1], [20]}
(%i3)  cardinality (s);
(%o3)                                 627
(%i4)  map (lambda ([x], apply ("+", x)), s);
(%o4)                                {20}
(%i5)  integer_partitions (20, 4);
(%o5) {[5, 5, 5, 5], [6, 5, 5, 4], [6, 6, 4, 4], [6, 6, 5, 3], [6, 6, 6, 2], 
[7, 5, 4, 4], [7, 5, 5, 3], [7, 6, 4, 3], [7, 6, 5, 2], [7, 6, 6, 1], 
[7, 7, 3, 3], [7, 7, 4, 2], [7, 7, 5, 1], [7, 7, 6, 0], [8, 4, 4, 4], 
[8, 5, 4, 3], [8, 5, 5, 2], [8, 6, 3, 3], [8, 6, 4, 2], [8, 6, 5, 1], 
[8, 6, 6, 0], [8, 7, 3, 2], [8, 7, 4, 1], [8, 7, 5, 0], [8, 8, 2, 2], 
[8, 8, 3, 1], [8, 8, 4, 0], [9, 4, 4, 3], [9, 5, 3, 3], [9, 5, 4, 2], 
[9, 5, 5, 1], [9, 6, 3, 2], [9, 6, 4, 1], [9, 6, 5, 0], [9, 7, 2, 2], 
[9, 7, 3, 1], [9, 7, 4, 0], [9, 8, 2, 1], [9, 8, 3, 0], [9, 9, 1, 1], 
[9, 9, 2, 0], [10, 4, 3, 3], [10, 4, 4, 2], [10, 5, 3, 2], [10, 5, 4, 1], 
[10, 5, 5, 0], [10, 6, 2, 2], [10, 6, 3, 1], [10, 6, 4, 0], [10, 7, 2, 1], 
[10, 7, 3, 0], [10, 8, 1, 1], [10, 8, 2, 0], [10, 9, 1, 0], [10, 10, 0, 0], 
[11, 3, 3, 3], [11, 4, 3, 2], [11, 4, 4, 1], [11, 5, 2, 2], [11, 5, 3, 1], 
[11, 5, 4, 0], [11, 6, 2, 1], [11, 6, 3, 0], [11, 7, 1, 1], [11, 7, 2, 0], 
[11, 8, 1, 0], [11, 9, 0, 0], [12, 3, 3, 2], [12, 4, 2, 2], [12, 4, 3, 1], 
[12, 4, 4, 0], [12, 5, 2, 1], [12, 5, 3, 0], [12, 6, 1, 1], [12, 6, 2, 0], 
[12, 7, 1, 0], [12, 8, 0, 0], [13, 3, 2, 2], [13, 3, 3, 1], [13, 4, 2, 1], 
[13, 4, 3, 0], [13, 5, 1, 1], [13, 5, 2, 0], [13, 6, 1, 0], [13, 7, 0, 0], 
[14, 2, 2, 2], [14, 3, 2, 1], [14, 3, 3, 0], [14, 4, 1, 1], [14, 4, 2, 0], 
[14, 5, 1, 0], [14, 6, 0, 0], [15, 2, 2, 1], [15, 3, 1, 1], [15, 3, 2, 0], 
[15, 4, 1, 0], [15, 5, 0, 0], [16, 2, 1, 1], [16, 2, 2, 0], [16, 3, 1, 0], 
[16, 4, 0, 0], [17, 1, 1, 1], [17, 2, 1, 0], [17, 3, 0, 0], [18, 1, 1, 0], 
[18, 2, 0, 0], [19, 1, 0, 0], [20, 0, 0, 0]}
(%i6)  integer_partitions (20, 4);
(%o6) {[5, 5, 5, 5], [6, 5, 5, 4], [6, 6, 4, 4], [6, 6, 5, 3], [6, 6, 6, 2], 
[7, 5, 4, 4], [7, 5, 5, 3], [7, 6, 4, 3], [7, 6, 5, 2], [7, 6, 6, 1], 
[7, 7, 3, 3], [7, 7, 4, 2], [7, 7, 5, 1], [7, 7, 6, 0], [8, 4, 4, 4], 
[8, 5, 4, 3], [8, 5, 5, 2], [8, 6, 3, 3], [8, 6, 4, 2], [8, 6, 5, 1], 
[8, 6, 6, 0], [8, 7, 3, 2], [8, 7, 4, 1], [8, 7, 5, 0], [8, 8, 2, 2], 
[8, 8, 3, 1], [8, 8, 4, 0], [9, 4, 4, 3], [9, 5, 3, 3], [9, 5, 4, 2], 
[9, 5, 5, 1], [9, 6, 3, 2], [9, 6, 4, 1], [9, 6, 5, 0], [9, 7, 2, 2], 
[9, 7, 3, 1], [9, 7, 4, 0], [9, 8, 2, 1], [9, 8, 3, 0], [9, 9, 1, 1], 
[9, 9, 2, 0], [10, 4, 3, 3], [10, 4, 4, 2], [10, 5, 3, 2], [10, 5, 4, 1], 
[10, 5, 5, 0], [10, 6, 2, 2], [10, 6, 3, 1], [10, 6, 4, 0], [10, 7, 2, 1], 
[10, 7, 3, 0], [10, 8, 1, 1], [10, 8, 2, 0], [10, 9, 1, 0], [10, 10, 0, 0], 
[11, 3, 3, 3], [11, 4, 3, 2], [11, 4, 4, 1], [11, 5, 2, 2], [11, 5, 3, 1], 
[11, 5, 4, 0], [11, 6, 2, 1], [11, 6, 3, 0], [11, 7, 1, 1], [11, 7, 2, 0], 
[11, 8, 1, 0], [11, 9, 0, 0], [12, 3, 3, 2], [12, 4, 2, 2], [12, 4, 3, 1], 
[12, 4, 4, 0], [12, 5, 2, 1], [12, 5, 3, 0], [12, 6, 1, 1], [12, 6, 2, 0], 
[12, 7, 1, 0], [12, 8, 0, 0], [13, 3, 2, 2], [13, 3, 3, 1], [13, 4, 2, 1], 
[13, 4, 3, 0], [13, 5, 1, 1], [13, 5, 2, 0], [13, 6, 1, 0], [13, 7, 0, 0], 
[14, 2, 2, 2], [14, 3, 2, 1], [14, 3, 3, 0], [14, 4, 1, 1], [14, 4, 2, 0], 
[14, 5, 1, 0], [14, 6, 0, 0], [15, 2, 2, 1], [15, 3, 1, 1], [15, 3, 2, 0], 
[15, 4, 1, 0], [15, 5, 0, 0], [16, 2, 1, 1], [16, 2, 2, 0], [16, 3, 1, 0], 
[16, 4, 0, 0], [17, 1, 1, 1], [17, 2, 1, 0], [17, 3, 0, 0], [18, 1, 1, 0], 
[18, 2, 0, 0], [19, 1, 0, 0], [20, 0, 0, 0]}
(%i7)  s: integer_partitions (20, 4);
(%o7) {[5, 5, 5, 5], [6, 5, 5, 4], [6, 6, 4, 4], [6, 6, 5, 3], [6, 6, 6, 2], 
[7, 5, 4, 4], [7, 5, 5, 3], [7, 6, 4, 3], [7, 6, 5, 2], [7, 6, 6, 1], 
[7, 7, 3, 3], [7, 7, 4, 2], [7, 7, 5, 1], [7, 7, 6, 0], [8, 4, 4, 4], 
[8, 5, 4, 3], [8, 5, 5, 2], [8, 6, 3, 3], [8, 6, 4, 2], [8, 6, 5, 1], 
[8, 6, 6, 0], [8, 7, 3, 2], [8, 7, 4, 1], [8, 7, 5, 0], [8, 8, 2, 2], 
[8, 8, 3, 1], [8, 8, 4, 0], [9, 4, 4, 3], [9, 5, 3, 3], [9, 5, 4, 2], 
[9, 5, 5, 1], [9, 6, 3, 2], [9, 6, 4, 1], [9, 6, 5, 0], [9, 7, 2, 2], 
[9, 7, 3, 1], [9, 7, 4, 0], [9, 8, 2, 1], [9, 8, 3, 0], [9, 9, 1, 1], 
[9, 9, 2, 0], [10, 4, 3, 3], [10, 4, 4, 2], [10, 5, 3, 2], [10, 5, 4, 1], 
[10, 5, 5, 0], [10, 6, 2, 2], [10, 6, 3, 1], [10, 6, 4, 0], [10, 7, 2, 1], 
[10, 7, 3, 0], [10, 8, 1, 1], [10, 8, 2, 0], [10, 9, 1, 0], [10, 10, 0, 0], 
[11, 3, 3, 3], [11, 4, 3, 2], [11, 4, 4, 1], [11, 5, 2, 2], [11, 5, 3, 1], 
[11, 5, 4, 0], [11, 6, 2, 1], [11, 6, 3, 0], [11, 7, 1, 1], [11, 7, 2, 0], 
[11, 8, 1, 0], [11, 9, 0, 0], [12, 3, 3, 2], [12, 4, 2, 2], [12, 4, 3, 1], 
[12, 4, 4, 0], [12, 5, 2, 1], [12, 5, 3, 0], [12, 6, 1, 1], [12, 6, 2, 0], 
[12, 7, 1, 0], [12, 8, 0, 0], [13, 3, 2, 2], [13, 3, 3, 1], [13, 4, 2, 1], 
[13, 4, 3, 0], [13, 5, 1, 1], [13, 5, 2, 0], [13, 6, 1, 0], [13, 7, 0, 0], 
[14, 2, 2, 2], [14, 3, 2, 1], [14, 3, 3, 0], [14, 4, 1, 1], [14, 4, 2, 0], 
[14, 5, 1, 0], [14, 6, 0, 0], [15, 2, 2, 1], [15, 3, 1, 1], [15, 3, 2, 0], 
[15, 4, 1, 0], [15, 5, 0, 0], [16, 2, 1, 1], [16, 2, 2, 0], [16, 3, 1, 0], 
[16, 4, 0, 0], [17, 1, 1, 1], [17, 2, 1, 0], [17, 3, 0, 0], [18, 1, 1, 0], 
[18, 2, 0, 0], [19, 1, 0, 0], [20, 0, 0, 0]}
(%i8)  cardinality (s);
(%o8)                                 108
(%i9)  xprimep(x) := integerp(x) and (x >
 1) and primep(x);
(%o9)         xprimep(x) := integerp(x) and (x > 1) and primep(x)
(%i10)  subset (s, lambda ([x], every (xprimep, x)));
(%o10) {[5, 5, 5, 5], [7, 5, 5, 3], [7, 7, 3, 3], [11, 3, 3, 3], 
                                                  [11, 5, 2, 2], [13, 3, 2, 2]}
(%i11) 
[abs,append,lambda,makelist,map,setify,sublist] [and,apply,cardinality,every,integer_partitions,integerp,lambda,map,subset] [and,cardinality,every,integer_partitions,integerp,lambda,primep,subset] [and,cardinality,every,integer_partitions,integerp,lambda,subset] [and,cos,do,if,lambda,print,sin] [and,every,integer_partitions,integerp,lambda,subset] [and,if,labels,lambda,let,not,or] [and,if,lambda,maplist] [append,assume,declare,eliminate,ev,first,fpprintprec,lambda,map,plot2d,solve,sublist] [append,atom,block,delete,do,emptyp,freeof,if,indices,lambda,length,lmax,lmin,makelist,map,member,not,parse_string,sdowncase,simplode,ssearch,string,sublist_indices,subst] [append,atom,block,delete,do,emptyp,freeof,if,indices,lambda,length,lmax,lmin,makelist,map,member,not,sublist_indices,subst] [append,atom,block,delete,flatten,if,lambda,load,map,return] [append,block,delete,do,emptyp,if,lambda,length,makelist,map,not,subst] [append,block,delete,flatten,lambda,length,makelist,map,return] [append,disjoin,first,if,lambda,listify,makelist,map,mod,setify,subset] [apply,args,block,col,copymatrix,do,genmatrix,map,mod,quotient,return,transpose] [apply,cardinality,integer_partitions,lambda,map] [apply,cons,lambda,let] [apply,equal,lambda,notequal,numberp] [atvalue,diff,ilt,lambda,laplace,map,solve] [bftorat,block,cons,delete,do,emptyp,first,float2bf,fpprec,lambda,last,listp,map,maplist,mod,ratepsilon,ratprint,rest,return,second] [bftorat,block,cons,delete,do,emptyp,first,float2bf,fpprec,lambda,last,listp,map,mod,ratepsilon,ratprint,rest,return] [bftorat,block,cons,delete,emptyp,false,first,float2bf,fpprec,if,integerp,kill,lambda,listp,map,mod,ratdenom,ratepsilon,ratprint,rest,return] [block,buildq,indices,lambda,macroexpand,map,sublist_indices] [block,cos,cot,csc,declare,evfun,if,kill,lambda,length,map,sec,sin,subst,tan] [block,delete,emptyp,if,lambda,length,makelist,map,not,subst] [block,do,indices,lambda,makelist,map,mod,print,sublist_indices] [buildq,first,lambda,map,second] [cardinality,every,integer_partitions,lambda,primep,subset] [cardinality,integer_partitions] [delete,every,full_listify,lambda,listify,makelist,map,mod,primep,set_partitions,sort,sublist] [diff,float,is,lambda,load,map,plot2d,rhs] [disjoin,first,if,lambda,listify,makelist,map,mod,setify,subset] [disjoin,first,if,lambda,makelist,map,mod,setify,subset] [do,evenp,first,if,lambda,makelist,map,return,setify,subset] [do,evenp,first,if,lambda,makelist,map,setify,subset] [eval_string,lambda,lreduce,map,permut,sort,string] [evenp,first,if,lambda,makelist,map,setify,subset] [evenp,first,lambda,makelist,map,setify,subset] [evenp,if,lambda,makelist,map,setify,subset] [evenp,lambda,makelist,map,setify,subset] [first,if,lambda,makelist,map,mod,setify,subset] [intersect,lambda,setdifference,sublist,subset,union] [jacobi,lambda,map] [lambda,linsolve,map,part] [lambda,load,map] [lambda,makelist,map,numer] [lambda,makelist,map,setify] [lambda,map] [lambda,sublist,subset]

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