#include <bits/stdc++.h>
using namespace std;
#define int long long
const int N = 2e5+5;
const int K = 3;
int vert[N][K+2];
int horz[K+2][N];
int prv[N][K+2];
int prh[K+2][N];
int A[2*N];
int pr1[2*N];
int sf1[2*N];
int pr2[2*N];
int sf2[2*N];
// N is the middle (N+i, N-i)
vector<long long> mosaic(vector<signed> X, vector<signed> Y, vector<signed> T, vector<signed> B, vector<signed> L, vector<signed> R) {
int n = X.size();
for (int i=0; i<n; i++) horz[1][i+1] = X[i];
for (int i=0; i<n; i++) vert[i+1][1] = Y[i];
for (int i=0; i<min(n, K); i++) horz[i+1][1] = Y[i];
for (int i=0; i<min(n, K); i++) vert[1][i+1] = X[i];
for (int i=2; i<=K+1; i++) {
for (int j=2; j<=n; j++) {
vert[j][i] = !vert[j-1][i] && !vert[j][i-1];
horz[i][j] = !horz[i-1][j] && !horz[i][j-1];
}
}
for (int i=0; i<=n; i++) A[N+i] = horz[K+1][K+1+i], A[N-i] = vert[K+1+i][K+1];
for (int i=1; i<=K; i++) {
for (int j=1; j<=n; j++) {
prv[j][i] = prv[j-1][i] + prv[j][i-1] - prv[j-1][i-1] + vert[j][i];
prh[i][j] = prh[i-1][j] + prh[i][j-1] - prh[i-1][j-1] + horz[i][j];
}
}
for (int i=1; i<2*N; i++) pr1[i] = pr1[i-1] + A[i];
for (int i=2*N-2; i>=0; i--) sf1[i] = sf1[i+1] + A[i];
for (int i=1; i<2*N; i++) pr2[i] = pr2[i-1] + pr1[i];
for (int i=2*N-2; i>=0; i--) sf2[i] = sf2[i+1] + sf1[i];
vector<int> res((int)T.size(), 0);
for (int q=0; q<T.size(); q++) {
int t = T[q]+1; int b=B[q]+1; int l=L[q]+1; int r=R[q]+1;
int pt = min(b, K);
// add t pt l r
if (t<=K) res[q] += prh[pt][r] - prh[t-1][r] - prh[pt][l-1] + prh[t-1][l-1];
if (t<=K) t = pt+1;
if (t > b) continue;
int pl = min(r, K);
// add t b l pl
if (l<=K) res[q] += prv[b][pl] - prv[t-1][pl] - prv[b][l-1] + prv[t-1][l-1];
if (l<=K) l = pl + 1;
if (l > r) continue;
int wsz = min(r - l + 1, b - t + 1);
int id1, id2;
// t b l r
int s = min(b, l); b-=s; l-=s;
if (b) id1 = N-b; else id1 = N+l;
s = min(t,r); t-=s; r-=s;
if (t) id2 = N - t; else id2 = N + r;
int j1 = id1 + wsz - 1;
int j2 = id2 - wsz + 1;
res[q] += wsz * (pr1[j2] - pr1[j1-1]);
j1--; j2++; if (j1 < id1 || j2 > id2) continue;
// id1 .. j1
// (id1) 1, 2, 3 ... - (j1+1) 1, 2, 3, ... - sf[j1+1] * (j1-id1+1))
res[q] += sf2[id1] - sf2[j1+1] - sf1[j1+1] * (j1-id1+1);
res[q] += pr2[id2] - pr2[j2-1] - pr1[j2-1] * (id2-j2+1);
}
return res;
}
