SAMPLE (Olympic 2021)

#include <bits/stdc++.h>
using namespace std;

int main() {
#ifdef LOCAL
    freopen("in.txt", "r", stdin);
#else
    freopen("SAMPLE.inp", "r", stdin);
    freopen("SAMPLE.out", "w", stdout);
#endif // LOCAL
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int n, m, k; cin >> n >> m >> k;
    map<int, int> cnt;
    while (n--) {
        string s; cin >> s;
        ++cnt[bitset<20>(s).to_ulong()];
/*
        int bs = 0;
        for (int i = 0; i < m; ++i)
            bs |= ((s[i] - '0') << i); // (s[i] - '0') dich di i bit
        ++cnt[bs];
*/
    }

    int64_t ans = 0;
    for (int mask1 = 0; mask1 <= (1 << m); ++mask1) {
        for (int mask2 = 0; mask2 <= (1 << m); ++mask2) {
            if (__builtin_popcountll(mask1 ^ mask2) == k) //Dem so bit bat cua (mask1 xor mask2 (giong 0, khac 1))
                ans += cnt[mask1] * cnt[mask2];
        }
    }

    cout << ans / 2 << '\n';

    return 0;
}