#include "mosaic.h"
#include<iostream>
#include<algorithm>
#include<vector>
#include<utility>
using namespace std;
typedef long long ll;
std::vector<long long> mosaic(std::vector<int> X, std::vector<int> Y, std::vector<int> T, std::vector<int> B, std::vector<int> L, std::vector<int> R){
int n = (int)X.size();
int q = (int)T.size();
vector<ll> ans(q);
if(n < 5){
vector<vector<int>> dp(n, vector<int>(n));
for(int i = 0; i < n; i++){
dp[0][i] = X[i];
dp[i][0] = Y[i];
}
for(int i = 1; i < n; i++){
for(int j = 1; j < n; j++){
if(dp[i - 1][j] == 0 && dp[i][j - 1] == 0) dp[i][j] = 1;
}
}
for(int i = 0; i < q; i++){
for(int j = T[i]; j <= B[i]; j++){
for(int k = L[i]; k <= R[i]; k++){
ans[i] += dp[j][k];
}
}
}
return ans;
}
vector<vector<ll>> dpx(6, vector<ll>(n + 1)), dpy(n + 1, vector<ll>(6)), prex(6, vector<ll>(n + 1)), prey(n + 1, vector<ll>(6));
for(int i = 0; i < n; i++){
dpx[1][i + 1] = X[i];
dpy[i + 1][1] = Y[i];
if(i < 5){
dpx[i + 1][1] = Y[i];
dpy[1][i + 1] = X[i];
}
}
for(int i = 2; i <= 5; i++){
for(int j = 2; j <= n; j++){
if(dpx[i - 1][j] == 0 && dpx[i][j - 1] == 0) dpx[i][j] = 1;
if(dpy[j - 1][i] == 0 && dpy[j][i - 1] == 0) dpy[j][i] = 1;
}
}
for(int i = 1; i <= 5; i++){
for(int j = 1; j <= n; j++){
prex[i][j] = prex[i - 1][j] + prex[i][j - 1] - prex[i - 1][j - 1] + dpx[i][j];
}
}
for(int i = 1; i <= n; i++){
for(int j = 1; j <= 5; j++){
prey[i][j] = prey[i - 1][j] + prey[i][j - 1] - prey[i - 1][j - 1] + dpy[i][j];
}
}
for(int i = 0; i < q; i++){
T[i]++;
B[i]++;
L[i]++;
R[i]++;
}
vector<ll> px1(n + 1), py1(n + 1), px2(n + 1), py2(n + 1);
for(int i = 5; i <= n; i++){
px1[i] = px1[i - 1] + dpx[5][i];
py1[i] = py1[i - 1] + dpy[i][5];
}
for(int i = 5; i <= n; i++){
px2[i] = px2[i - 1] + px1[i];
py2[i] = py2[i - 1] + py1[i];
}
auto get = [&](int x, int y){
if(x <= 5) return prex[x][y];
if(y <= 5) return prey[x][y];
ll res = prex[4][y] + prey[x][4] - prex[4][4];
int w = min(x - 4, y - 4);
res -= dpx[5][5] * w;
res += px2[y] - px2[y - w];
res += py2[x] - py2[x - w];
return res;
};
for(int i = 0; i < q; i++){
ans[i] = get(B[i], R[i]) - get(B[i], L[i] - 1) - get(T[i] - 1, R[i]) + get(T[i] - 1, L[i] - 1);
}
return ans;
}
