Codeforces Round #257 (Div. 1) D - Jzzhu and Numbers 容斥原理 + SOS dp

#include<bits/stdc++.h>
#define LL long long
#define fi first
#define se second
#define mk make_pair
#define PLL pair<LL, LL>
#define PLI pair<LL, int>
#define PII pair<int, int>
#define SZ(x) ((int)x.size())
#define ull unsigned long long
using namespace std;

const int N = 1e6 + 7;
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3f;
const int mod = 1e9 + 7;
const double eps = 1e-8;

int cnt[1<<20], bin[N], num[1<<20], n;

int main() {
    for(int i = bin[0] = 1; i < N; i++) bin[i] = bin[i - 1] * 2 % mod;
    scanf("%d", &n);
    for(int i = 1; i <= n; i++) {
        int x; scanf("%d", &x);
        cnt[x]++;
    }
    for(int i = 0; i < 20; i++)
        for(int S = 0; S < (1 << 20); S++)
            if(S >> i & 1) cnt[S ^ (1 << i)] += cnt[S];
    LL ans = bin[n];
    for(int S = 1; S < (1 << 20); S++) {
        num[S] = num[S-(S&-S)] + 1;
        if(num[S] & 1) ans = (ans - bin[cnt[S]] + mod) % mod;
        else ans = (ans + bin[cnt[S]]) % mod;
    }
    printf("%lld\n", ans);
    return 0;
}

/*
*/