//chockolateman
#include<bits/stdc++.h>
using namespace std;
int N,status[100][100][1000],col[100][100];
pair<int,int> info[100][100][1000]; //info[i][j][k] = shows that for (i,j) the kth bit has info for info[i][j][k]
pair<pair<int,int>,int> take_it_from[100][100][1000];
int s_i[100][100];
bool found[100][100];
void calc_info()
{
if(N <= 10)
{
for(int i = 0 ; i < N ; i+=2)
for(int j = 0 ; j < N ; j++)
if(j%2==1)
col[i][j] = 1;
else
col[i][j] = 2;
for(int i = 1 ; i < N ; i+=2)
for(int j = 0 ; j < N ; j++)
if(j%2==1)
col[i][j] = 3;
else
col[i][j] = 4;
}
else
{
for(int j = 0 ; j < N ; j++)
if(j%2==1)
col[0][j] = 1;
else
col[0][j] = 2;
for(int j = 0 ; j < N ; j++)
if(j%2==1)
col[1][j] = 3;
else
col[1][j] = 4;
int turn = 5;
for(int i = 2 ; i < N ; i++)
{
int other = 1;
for(int j = 0 ; j < N ; j++)
if(j%2==1)
{
col[1][j] = other;
other++;
if(other==turn)
other++;
if(other==6)
other = 1;
if(other==turn)
other++;
}
else
col[1][j] = turn;
turn++;
if(turn==6)
turn = 1;
}
}
for(int i = 0 ; i < N ; i++)
for(int j = 0 ; j < N ; j++)
{
s_i[i][j] = 1;
info[i][j][0] = {i,j};
}
for(int i = N-1 ; i >= 0 ; i--)
for(int j = N-1 ; j >= 0 ; j--)
{
for(int x = 0 ; x < N ; x++)
for(int y = 0 ; y < N ; y++)
found[x][y] = false;
found[i][j] = true;
take_it_from[i][j][0] = {{i,j},0};
int cur_pos = 1;
for(int x = i+2 ; x >= i ; x--)
for(int y = j+2 ; y >= j ; y--)
{
if(x==i && y==j)
continue;
s_i[i][j] += s_i[x][y];
for(int l = 0 ; l < s_i[x][y] ; l++)
{
if(found[info[x][y][l].first][info[x][y][l].second] || (col[i][j] != col[x][y]))
{
s_i[i][j]--;
continue;
}
info[i][j][cur_pos++] = info[x][y][l];
take_it_from[i][j][cur_pos - 1] = {{x,y},l};
found[info[x][y][l].first][info[x][y][l].second] = true;
}
}
if(s_i[i][j] > 100)
printf("FUCK\n");
}
}
int grid[100][100],di[4] = {1,-1,0,0},dj[4] = {0,0,1,-1};
bool visited[100][100];
void dfs(int i,int j)
{
if(i < 0 || i >= N || j < 0 || j >= N)
return;
if(visited[i][j])
return;
visited[i][j] = true;
for(int k = 0 ; k <= 3 ; k++)
{
int x = i + di[k];
int y = j + dj[k];
dfs(x,y);
}
}
long long solve()
{
memset(visited,false,sizeof(visited));
for(int i = 0 ; i < N ; i++)
for(int j = 0 ; j < N ; j++)
if(grid[i][j]==0)
visited[i][j] = true;
int ret = 0;
for(int i = 0 ; i < N ; i++)
for(int j = 0 ; j < N ; j++)
if(!visited[i][j])
{
ret++;
dfs(i,j);
}
return ret;
}
std::string process(std::vector <std::vector<std::string>> a, int i, int j, int k, int n)
{
N = 2*n + 1;
calc_info();
std::string ret(100 ,'0');
for(int l = 0 ; l < s_i[i][j] ; l++)
{
int x = take_it_from[i][j][l].first.first;
int y = take_it_from[i][j][l].first.second;
int r = take_it_from[i][j][l].second;
status[i][j][l] = a[x-i][y-j][r] - '0';
ret[l] = a[x-i][y-j][r];
}
if(k==n-1)
{
for(int r = 0 ; r <= 2 ; r++)
for(int s = 0 ; s <= 2 ; s++)
{
if(r==0 && s==0)
continue;
for(int l = 0 ; l < s_i[i][j] ; l++)
status[r][s][l] = a[r-i][s-i][l] - '0';
}
while(i <= 2)
{
j = 0;
while(j <= 2)
{
for(int l = 0 ; l < s_i[i][j] ; l++)
{
int x = info[i][j][l].first;
int y = info[i][j][l].second;
grid[x][y] = status[i][j][l];
}
j++;
}
i++;
}
int ans = solve();
int pos = 0;
for(int l = 0 ; l <= 99 ; l++)
{
ret[l] = ans%2 + '0';
ans /= 2;
}
}
return ret;
}
