#include <bits/stdc++.h>
using namespace std;
vector<long long> mosaic(vector<int> X, vector<int> Y, vector<int> T, vector<int> B, vector<int> L, vector<int> R) {
int N = X.size();
vector<int> fr(N), sr(N), tr(N);
vector<int> fc(N), sc(N), tc(N);
fr = X;
fc = Y;
sr[0] = fc[1];
for (int i = 1; i < N; i++) sr[i] = !(fr[i]||sr[i-1]);
tr[0] = fc[2];
for (int i = 1; i < N; i++) tr[i] = !(sr[i]||tr[i-1]);
sc[0] = fr[1];
for (int i = 1; i < N; i++) sc[i] = !(fc[i]||sc[i-1]);
tc[0] = fr[2];
for (int i = 1; i < N; i++) tc[i] = !(sc[i]||tc[i-1]);
vector<int> diag(2*N);
int a = 0;
for (int i = N-1; i > 2; i--) diag[a++] = tc[i];
for (int i = 2; i < N; i++) diag[a++] = tr[i];
auto prefixa = [&](vector<int> &a, vector<long long> &p) {
p.resize(a.size()+1);
p[0] = 0;
for (int i = 0; i < N; i++) p[i+1] = p[i]+a[i];
};
vector<long long> pfr, pfc, psr, psc, pdiag;
prefixa(fr, pfr); prefixa(fc, pfc); prefixa(sr, psr); prefixa(sc, psc); prefixa(diag, pdiag);
int M = T.size();
vector<long long> ans(M, 0);
for (int i = 0; i < M; i++) {
if (T[i] == 0) ans[i] = pfr[R[i]+1]-pfr[L[i]];
else if (T[i] == 1) ans[i] = psr[R[i]+1]-psr[L[i]];
else {
if (L[i] == 0) {
ans[i] += fc[T[i]];
L[i]++;
if (R[i] == 0) continue;
}
if (L[i] == 1) {
ans[i] += sc[T[i]];
L[i]++;
if (R[i] == 1) continue;
}
int di = L[i]-T[i]+N-3, df = R[i]-T[i]+N-3;
ans[i] += pdiag[df+1]-pdiag[di];
}
}
return ans;
}
