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// @Title: 好子集的数目 (The Number of Good Subsets)
// @Author: 15816537946@163.com
// @Date: 2022-02-22 15:26:55
// @Runtime: 196 ms
// @Memory: 8.1 MB
var primes = []int{2, 3, 5, 7, 11, 13, 17, 19, 23, 29}

func numberOfGoodSubsets(nums []int) (ans int) {
    const mod int = 1e9 + 7
    freq := [31]int{}
    for _, num := range nums {
        freq[num]++
    }

    f := make([]int, 1<<len(primes))
    f[0] = 1
    for i := 0; i < freq[1]; i++ {
        f[0] = f[0] * 2 % mod
    }
next:
    for i := 2; i < 31; i++ {
        if freq[i] == 0 {
            continue
        }

        // 检查 i 的每个质因数是否均不超过 1 个
        subset := 0
        for j, prime := range primes {
            if i%(prime*prime) == 0 {
                continue next
            }
            if i%prime == 0 {
                subset |= 1 << j
            }
        }

        // 动态规划
        for mask := 1 << len(primes); mask > 0; mask-- {
            if mask&subset == subset {
                f[mask] = (f[mask] + f[mask^subset]*freq[i]) % mod
            }
        }
    }

    for _, v := range f[1:] {
        ans = (ans + v) % mod
    }
    return
}