#include <bits/stdc++.h>
using namespace std;
int was[10000];
int arr[100][100];
vector < int > g[100];
void dfs(int v){
was[v] = 1;
for(int u : g[v])
if(!was[u])
dfs(u);
}
string process(vector < vector < string > > a, int i, int j, int k, int n){
string s;
for(int x = 0; x < 3; x++){
for(int y = 0; y < 3; y++){
if(i + x < 2 * (n - k - 1) && j + y < 2 * (n - k - 1)){
while(a[x][y].size() > 1) a[x][y].pop_back();
}
else if(i + x >= 2 * (n - k - 1) && j + y >= (2 * (n - k - 1))){
while(a[x][y].size() > (2 * k + 1) * (2 * k + 1)) a[x][y].pop_back();
}
else{
while(a[x][y].size() > (2 * k + 1)) a[x][y].pop_back();
}
}
}
if(i < 2 * (n - k - 1) && j < 2 * (n - k - 1)){
s = a[0][0];
}
else if(i < 2 * (n - k - 1)){
s = a[0][0] + a[0][1] + a[0][2];
}
else if(j < 2 * (n - k - 1)){
s = a[0][0] + a[1][0] + a[2][0];
}
else{
s = a[0][0] + a[0][1] + a[0][2] + a[1][0] + a[1][1] + a[1][2] + a[2][0] + a[2][1] + a[2][2];
}
if(k == n - 1){
n = 2 * n + 1;
for(int i = 0; i < n; i++)
for(int j = 0; j < n; j++)
arr[i][j] = s[i * n + j] - '0';
for(int i = 0; i < n; i++){
for(int j = 0; j < n; j++){
if(!arr[i][j]) continue;
int v = i * n + j;
if(i > 0 && arr[i - 1][j]) g[v].push_back(v - n);
if(j > 0 && arr[i][j - 1]) g[v].push_back(v - 1);
if(i < n - 1 && arr[i + 1][j]) g[v].push_back(v + n);
if(j < n - 1 && arr[i][j + 1]) g[v].push_back(v + 1);
}
}
int ans = 0;
for(int i = 0; i < n * n; i++){
if(!was[i] && arr[i / n][i % n]){
dfs(i), ans++;
}
}
s.clear();
for(int i = 0; i < 30; i++) s.push_back(('0' + (ans >> i & 1)));
while(s.size() < 100) s.push_back('0');
return s;
}
while(s.size() < 100) s.push_back('0');
return s;
}
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