#include "mosaic.h"
#include <iostream>
#include <iomanip>
#include <string>
#include <math.h>
#include <algorithm>
#include <cstring>
#include <numeric>
#include <vector>
#include <bitset>
#include <map>
#include <set>
#include <queue>
#include <deque>
#include <stack>
#include <unordered_map>
#include <unordered_set>
#include <cassert>
using namespace std;
#define dbg(x) cerr<<#x<<": "<<x<<"\n";
/*
ValeNotta lover
*/
vector<long long> mosaic(vector<int> X, vector<int> Y, vector<int> T, vector<int> B, vector<int> L, vector<int> R) {
int n=(int)X.size();
vector<vector<long long>>dp(n+1);
for(int i=0 ; i<=n ; i++) dp[0].push_back(0);
for(int i=1 ; i<=n ; i++){
dp[i].push_back(0);
for(int j=1 ; j<=n ; j++){
if(i==1) dp[i].push_back(X[j-1]);
else if(j==1) dp[i].push_back(Y[i-1]);
else{
if(i>=4 && j>=4) break;
if(dp[i-1][j]==0 && dp[i][j-1]==0) dp[i].push_back(1);
else dp[i].push_back(0);
}
// dbg(dp[i].back())
}
}
set<int>cast;
for(int i=1 ; i<=n ; i++){
for(int j=1 ; j<=n ; j++){
if(i>=4 && j>=4) break;
if(i==3 || j==3){
if(dp[i][j]==1) cast.insert(i-j);
}
// cout<<dp[i][j]<<" ";
dp[i][j]+=dp[i-1][j]+dp[i][j-1]-dp[i-1][j-1];
}
// cout<<"\n";
}
// cout<<"\n\n";
vector<long long>pref;
pref.push_back(0);
for(int i=1-n ; i<=n-1 ; i++){
if(cast.find(i)!=cast.end()) pref.push_back(pref.back()+1);
else pref.push_back(pref.back());
}
int N=(int)T.size();
vector<long long>ans(n, 0);
for(int i=0 ; i<N ; i++){
T[i]++; B[i]++; L[i]++; R[i]++;
if(R[i]<=3 || B[i]<=3){
ans[i]=dp[B[i]][R[i]]-dp[T[i]-1][R[i]]-dp[B[i]][L[i]-1]+dp[T[i]-1][L[i]-1];
}else{
if(L[i]<=3){
ans[i]=dp[B[i]][3]-dp[T[i]-1][3]-dp[B[i]][L[i]-1]+dp[T[i]-1][L[i]-1];
L[i]=4;
}
int r=T[i]-L[i], l=T[i]-R[i];
ans[i]+=pref[r]-pref[l+n-1];
}
}
return ans;
}
