#include #include class Solution { private: inline static const int primes[] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}; inline static const int MOD = 1000000007; public: static int numberOfGoodSubsets(const std::vector& nums) { int cnt[31]{}; for (int i : nums) ++cnt[i]; // 2 x 3 = 6 // 2 x 5 = 10 // 2 x 7 = 14 // 2 x 11 = 22 // 2 x 13 = 26 // 3 x 5 = 15 // 3 x 7 = 21 long long ret = 0; for (int i = 1; i < 1024; ++i) { // Original numbers long long now = 1; for (int j = 0; j < 10; ++j) if (i & (1 << j)) now = (now * cnt[primes[j]]) % MOD; ret = (ret + now) % MOD; if (i & 1) { // 2-related numbers for (int j = 1; j <= 5; ++j) { if ((i & (1 << j)) && (now = cnt[primes[j] << 1])) { // Now, there is no 2, no primes[j], but (primes[j] << 1). for (int k = 1; k < 10; ++k) if (k != j && (i & (1 << k))) now = (now * cnt[primes[k]]) % MOD; ret = (ret + now) % MOD; } } } if (i & 2) { // 3-related numbers // Only 5 (indexed 2) and 7 (indexed 3) is valid. if ((i & 4) && (now = cnt[15])) { for (int k = 0; k < 10; ++k) if (k != 1 && k != 2 && (i & (1 << k))) now = (now * cnt[primes[k]]) % MOD; ret = (ret + now) % MOD; } if ((i & 8) && (now = cnt[21])) { for (int k = 0; k < 10; ++k) if (k != 1 && k != 3 && (i & (1 << k))) now = (now * cnt[primes[k]]) % MOD; ret = (ret + now) % MOD; } } if ((now = cnt[30]) && ((i & 7) == 7)) { // 2 * 3 * 5 == 30 for (int j = 3; j < 10; ++j) if (i & (1 << j)) now = (now * cnt[primes[j]]) % MOD; ret = (ret + now) % MOD; } // 2 - (11, 13) + 3 - (5, 7) if (((i & 3) == 3) && (i & 61)) { for (int j2 = 2; j2 <= 5; ++j2) { for (int j3 = 2; j3 <= 3; ++j3) { if (j2 != j3 && (i & (1 << j2)) && (i & (1 << j3))) { now = (cnt[primes[j2] << 1] * cnt[primes[j3] * 3]) % MOD; for (int k = 2; k < 10; ++k) { if (k != j2 && k != j3 && (i & (1 << k))) { now = (now * cnt[primes[k]]) % MOD; } } ret = (ret + now) % MOD; } } } } } while (cnt[1]--) { ret = (ret << 1) % MOD; } return ret % MOD; } }; int main() { std::cout << Solution::numberOfGoodSubsets({5, 10, 1, 26, 24, 21, 24, 23, 11, 12, 27, 4, 17, 16, 2, 6, 1, 1, 6, 8, 13, 30, 24, 20, 2, 19}); return 0; }