#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#pragma GCC optimize ("Ofast")
#pragma GCC target ("avx2")
#include "coprobber.h"
using namespace std;
using namespace __gnu_pbds;
using ll = long long;
using ld = long double;
using ii = pair<ll, ll>;
using ull = unsigned long long;
using vl = vector<long long>;
#define mp make_pair
#define pb push_back
#define pp pop_back
#define ff first
#define ss second
#define lb lower_bound
#define ub upper_bound
#define all(x) (x).begin() , (x).end()
#define vi vector<int>
const int N = 2*100005;
const long long MOD = 1000000007;
const long double EPS = 0.000000001;
const double PI = 3.14159265358979323846;
const long long INF = 10000000000000000;
long long gcd(int a, int b) { return (b==0?a:gcd(b, a%b)); }
long long lcm(int a, int b) { return a*(b/gcd(a, b)); }
long long fact(int a) { return (a==1?1:a*fact(a-1)); }
template<class T> using Tree = tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>;
#define MAX_N 500
vector<int>adj[MAX_N];
int police = 0, r, c; bool grid = 0;
bitset<524>prime;
void init() {
prime[1] = prime[0] = 1;
for(int l = 2; l <= 500; l++) {
for(int i = 2; i * l <= 500; i++)
prime[l*i] = 1;
}
}
bool isgrid(int N) {
if(!prime[N]) return 0;
int a = 0, b = 0, c = 0;
for(int l = 0; l < N; l++) {
int sz = (int)adj[l].size();
a+=(sz==2);
b+=(sz==3);
c+=(sz==4);
}
if(a!=4||a+b+c!=N) return 0;
bool ok = 0;
for(int l = 2; l * l <= N; l++) {
if(N % l) continue;
int curr = l*2 + (N/l)*2 - 4;
ok |= ((curr == a + b) && (c == N - curr));
}
return ok;
}
int start(int N, bool A[MAX_N][MAX_N])
{
for(int l = 0; l < N; l++) {
for(int i=0; i < N; i++) {
if(A[l][i]) adj[l].pb(i);
}
}
c = adj[0][1];
r = N/c;
grid = isgrid(N);
return 0;
}
const int nx[4] = {0, 0, 1, -1}, ny[4] = {1, -1, 0, 0};
int dist(int x, int y, int a, int b) { return abs(x-a)+abs(y-b); }
bool dfs(int v, int p, int dest) {
if(v == dest) return 1;
for(auto u:adj[v]) {
if(u == p) continue;
if(dfs(u, v, dest)) return 1;
}
return 0;
}
int nextMove(int R)
{
if(grid) {
int r1 = police / c, r2 = R / c;
int c1 = police % c, c2 = R % c;
int a = abs(r1 - r2), b = abs(c1 - c2);
if(a < b) {
int curr = 1e9, xx, yy;
for(int l = 0; l < 2; l++) {
int x = r1 + nx[l], y = c1 + ny[l];
int d = dist(x, y, r2, c1);
if(d < curr) xx = x, yy = y, curr = d;
}
return police = xx * c + yy;
}
else if(a > b) {
int curr = 1e9, xx, yy;
for(int l = 2; l < 4; l++) {
int x = r1 + nx[l], y = c1 + ny[l];
int d = dist(x, y, r2, c1);
if(d < curr) xx = x, yy = y, curr = d;
}
return police = xx * c + yy;
}
else if(a == b) return police;
}
else {
for(auto u:adj[police]) {
if(u==R||dfs(u, police, R)) {
return police = u;
}
}
}
}
