This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#define ll long long
using namespace std;
const int N = 18;
const int mod = 998244353;
bool isindep[1<<N];
ll dp[1<<N];
int popcnt[1<<N];
int undirected_edge[N];
int main(){
int n,m,a,b;
cin >> n >> m;
for(int i = 1; i <= m; i++){
cin >> a >> b;
a--;b--;
undirected_edge[a] ^= (1<<b);
undirected_edge[b] ^= (1<<a);
}
for(int i = 0; i < (1<<n); i++){
int edges = 0;
for(int j = 0; j < n; j++){
if(i&(1<<j)){
popcnt[i]++;
edges |= undirected_edge[j];
}
}
if((edges&i) == 0) isindep[i] = true;
}
dp[0] = 1;
for(int i = 1; i < (1<<n); i++){
for(int j = i; j >= 0; j = (j-1)&i){
if(isindep[j]){
if(popcnt[j]&1) dp[i] += dp[i^j];
else dp[i] -= dp[i^j];
}
}
dp[i]%=mod;
}
ll ans = dp[(1<<n)-1];
if(ans&1) ans += mod;
ans >>= 1;
ans *= m; ans %= mod;
cout << ans;
return 0;
}
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