#include "mosaic.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
using vi =vector<int>;
using vl = vector<ll>;
using vvi = vector<vi>;
using vvl = vector<vl>;
using pi = pair<int, int>;
using vpi = vector<pi>;
#ifdef LOCAL
#define dout std::cout
#else
#define dout if (0) std::cout
#endif
#define pb push_back
#define lb lower_bound
#define ub upper_bound
#define all(x) (x).begin(), (x).end()
#define en(x) (x).end()
#define bg(x) (x).begin()
#define rev(x) reverse(all(x))
#define sz(x) int((x).size())
#define FOR(i, a, b) for (int i = a; i < b; i++)
#define each(a, x) for (auto &a : x)
#define trace(x) for (auto &el : x) dout << el << " "
vl mosaic(vi X, vi Y, vi T, vi B, vi L, vi R) {
int Q = sz(T), n = sz(X);
if (n <= 5000) {
vl C(Q, 0);
vvi grid(n, vi(n, 0));
FOR(i, 0, n) {
grid[0][i] = X[i];
grid[i][0] = Y[i];
}
FOR(i, 1, n) {
FOR(j, 1, n) {
if (grid[i-1][j] == 0 && grid[i][j-1] == 0) grid[i][j] = 1;
else grid[i][j] = 0;
}
}
vvl pref(n+1, vl(n+1, 0));
FOR(i, 0, n) {
FOR(j, 0, n) {
pref[i+1][j+1] = grid[i][j] + pref[i+1][j];
}
FOR(j, 0, n) {
pref[i+1][j+1] += pref[i][j+1];
}
}
// vl prefx(n+1, 0); FOR(i, 0, n) prefx[i+1] = prefx[i] + X[i];
FOR(qn, 0, Q) {
int x1 = T[qn], x2 = B[qn], y1 = L[qn], y2 = R[qn];
// C[qn] = prefx[y2+1] - prefx[y1];
C[qn] += pref[x2+1][y2+1];
C[qn] += pref[x1][y1];
C[qn] -= pref[x1][y2+1];
C[qn] -= pref[x2+1][y1];
}
return C;
}
vl C(Q, 0);
vvi grid(n, vi(3, 0)); grid[0].resize(n); grid[1].resize(n); grid[2].resize(n);
FOR(i, 0, n) {
grid[0][i] = X[i];
grid[i][0] = Y[i];
}
map<pi, int> coord;
map<int, pi> revcoord;
int cc = 0;
for (int i = n - 1; i >= 3; i--) {
coord[{i, 2}] = cc++;
revcoord[cc-1] = {i, 2};
}
for (int i = 2; i < n; i++) {
coord[{2, i}] = cc++;
revcoord[cc-1] = {2, i};
}
FOR(i, 1, n) {
int top = i <= 2 ? n : 3;
FOR(j, 1, top) {
if (grid[i-1][j] == 0 && grid[i][j-1] == 0) grid[i][j] = 1;
else grid[i][j] = 0;
}
}
vl pref(cc+1, 0);
FOR(i, 0, cc) pref[i+1] = pref[i] + grid[revcoord[i].first][revcoord[i].second];
vl wpref(cc+1, 0); FOR(i, 1, cc+1) wpref[i] = wpref[i-1] + i * grid[revcoord[i-1].first][revcoord[i-1].second];
vl wrpref(cc+1, 0); FOR(i, 1, cc+1) wrpref[i] = wrpref[i-1] + i * grid[revcoord[cc-i].first][revcoord[cc-i].second];
vvl prefix(n+1, vl(4, 0)); prefix[0].resize(n+1); prefix[1].resize(n+1); prefix[2].resize(n+1); prefix[3].resize(n+1);
FOR(i, 0, n) {
int top = i < 3 ? n : 3;
FOR(j, 0, top) {
prefix[i+1][j+1] = grid[i][j] + prefix[i+1][j];
}
FOR(j, 0, top) {
prefix[i+1][j+1] += prefix[i][j+1];
}
}
auto get_ramp_up = [&](int u, int len) {
int v = u + len - 1;
ll sumVal = pref[v+1] - pref[u];
ll sum_iVal = (wpref[v+1] - wpref[u]) - sumVal;
return sum_iVal - ll(u-1) * sumVal;
};
auto get_ramp_down = [&](int e, int len) {
int s = e - len + 1;
ll sumVal = pref[e+1] - pref[s];
ll sum_iVal = (wpref[e+1] - wpref[s]) - sumVal;
return sum_iVal + ll(len - e) * sumVal;
};
for (int qn = 0; qn < Q; ++qn) {
int x1 = T[qn], x2 = B[qn];
int y1 = L[qn], y2 = R[qn];
ll res = 0;
if (x1 <= 2) {
int r = min(x2, 2);
res += prefix[r+1][y2+1]
- prefix[r+1][y1]
- prefix[x1][y2+1]
+ prefix[x1][y1];
}
if (y1 <= 2) {
int c = min(y2, 2);
res += prefix[x2+1][c+1]
- prefix[x1][c+1]
- prefix[x2+1][y1]
+ prefix[x1][y1];
}
if (x1 <= 2 && y1 <= 2) {
res -= prefix[x1][y1];
}
int cx = max(x1, 3), cy = max(y1, 3);
if (cx <= x2 && cy <= y2) {
int diagLen = min(x2 - cx, y2 - cy) + 1;
int sx = cx - (diagLen - 1),
sy = cy - (diagLen - 1);
int ex = cx, ey = cy;
int lc = coord[{sx, sy}],
rc = coord[{ex, ey}];
ll rise = get_ramp_up(lc, diagLen);
ll flat = 0;
int fl = lc + diagLen,
fr = rc - diagLen;
if (fl <= fr) {
ll cnt = fr - fl + 1;
ll segment= pref[fr+1] - pref[fl];
flat = cnt * segment;
}
ll fall = get_ramp_down(rc, diagLen);
res += rise + flat + fall;
}
C[qn] = res;
}
return C;
}
