#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> ii;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<ii> vii;
typedef vector<ll> vll;
typedef vector<pll> vpll;
#define PB push_back
#define PF push_front
#define PPB pop_back
#define PPF pop_front
#define X first
#define Y second
#define MP make_pair
#define all(x) (x).begin(), (x).end()
const int mod = 1e9 + 7; //998244353;
const int inf = 1e9 + 7;
const ll INF = 1e18 + 7;
const int logo = 20;
const int MAXN = 1e6 + 7;
const int off = 1 << logo;
const int trsz = off << 1;
const int dx[] = {1, -1, 0, 0};
const int dy[] = {0, 0, -1, 1};
vi coin_flips(vi vec, int ja){
int xr = 0;
for(int i=0; i<64; i++) if(vec[i]) xr ^= i;
int nd = ja ^ xr;
vec[nd] ^= 1;
return vec;
}
int find_coin(vi vec){
int xr = 0;
for(int i=0; i<64; i++) if(vec[i]) xr ^= i;
return xr;
}
