#include "mosaic.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ari2 = array<int, 2>;
using ari3 = array<int, 3>;
using arl2 = array<ll, 2>;
using arl3 = array<ll, 3>;
template <class T> using vt = vector<T>;
#define all(x) begin(x), end(x)
#define size(x) (int((x).size()))
#define REP(a,b,c,d) for(int a=(b);(d)>0?a<=(c):a>=(c);a+=(d))
#define FOR(a,b,c) REP(a,b,c,1)
#define ROF(a,b,c) REP(a,b,c,-1)
constexpr int mxN = 200005;
struct ST {
int val;
ST *lft, *rht;
void update(const int i, const int v, const int tl = -mxN, const int tr = mxN) {
if (tl == tr)
val = v;
else {
int tm = (tl + tr) / 2;
tm -= tm == tr;
if (i <= tm) {
if (!lft)
lft = new ST{0, nullptr, nullptr};
lft->update(i, v, tl, tm);
} else {
if (!rht)
rht = new ST{0, nullptr, nullptr};
rht->update(i, v, tm+1, tr);
}
val = (lft ? lft->val : 0) + (rht ? rht->val : 0);
}
}
int query(const int ql, const int qr, const int tl = -mxN, const int tr = mxN) {
if (tl > qr || tr < ql)
return 0;
if (ql <= tl && tr <= qr)
return val;
int tm = (tl + tr) / 2;
tm -= tm == tr;
return (lft ? lft->query(ql, qr, tl, tm) : 0) + (rht ? rht->query(ql, qr, tm+1, tr) : 0);
}
};
vt<ll> mosaic(vt<int> X, vt<int> Y, vt<int> T, vt<int> B, vt<int> L, vt<int> R) {
const int N = size(X), Q = size(T);
if (false && N <= 5000) {
vt<vt<int>> grid(N+1, vt<int>(N+1));
FOR(i, 1, N) {
grid[1][i] = X[i-1];
grid[i][1] = Y[i-1];
}
vt<vt<int>> psum(N+1, vt<int>(N+1));
FOR(i, 1, N)
FOR(j, 1, N) {
if (i > 1 && j > 1)
grid[i][j] = !grid[i-1][j] & !grid[i][j-1];
psum[i][j] = psum[i-1][j] + psum[i][j-1] - psum[i-1][j-1] + grid[i][j];
}
vt<ll> ret(Q);
FOR(i, 0, Q-1)
ret[i] = psum[B[i]+1][R[i]+1] - psum[B[i]+1][L[i]] - psum[T[i]][R[i]+1] + psum[T[i]][L[i]];
return ret;
}
if (*max_element(all(B)) == 0) {
vt<int> psum(N+1);
FOR(i, 0, N-1)
psum[i+1] = psum[i] + X[i];
vt<ll> ret(Q);
FOR(i, 0, Q-1)
ret[i] = psum[R[i]+1] - psum[L[i]];
return ret;
}
if (*max_element(all(X)) == 0 && *max_element(all(Y)) == 0) {
vt<ll> ret(Q);
FOR(i, 0, Q-1) {
L[i] += !L[i];
T[i] += !T[i];
ret[i] = (1ll * (B[i] - T[i] + 1) * (R[i] - L[i] + 1) + (T[i] + L[i] + 1 & 1)) / 2;
}
return ret;
}
vt<vt<int>> queries(N);
FOR(i, 0, Q-1)
queries[T[i]].push_back(i);
vt<int> psum(N);
psum[0] = X[0];
FOR(i, 1, N-1)
psum[i] = psum[i-1] + X[i];
const auto transform = [&](const int y, const int n) {
const vt<int> temp(X.begin(), X.begin() + n);
psum[0] = X[0] = Y[y];
FOR(i, 1, n-1) {
X[i] = !X[i-1] & !temp[i];
psum[i] = psum[i-1] + X[i];
}
};
vt<ll> ret(Q);
for (const auto &i : queries[0])
ret[i] = psum[R[i]] - (L[i] ? psum[L[i]-1] : 0);
if (N == 1)
return ret;
transform(1, N);
for (const auto &i : queries[1])
ret[i] = psum[R[i]] - (L[i] ? psum[L[i]-1] : 0);
if (N == 2)
return ret;
transform(2, N);
ST *st = new ST{0, nullptr, nullptr};
set<int> zeros;
FOR(i, 2, N-2)
if (X[i] == X[i+1]) {
assert(!X[i]);
zeros.insert(i);
st->update(i, 1);
}
FOR(i, 2, N-1) {
if (X[0] == X[1])
zeros.insert(-i + 2), st->update(-i + 2, 1);
else if (X[1] == X[2])
zeros.insert(-i + 3), st->update(-i + 3, 1);
for (const auto &j : queries[i]) {
const auto pp = [&](const int x) {
if (x < 0)
return 0;
int res = 0;
auto a = zeros.lower_bound(-i + 2);
auto b = zeros.lower_bound(x - i + 3);
if (a == b)
res += (x + 1 + X[0]) / 2;
if (a != b && *a + i - 2 < x) { // between a and b
const int l = *a, r = *prev(b);
res += (r - l - st->query(l+1, r)) / 2;
}
if (b != a && *prev(b) + i <= x) { // b to x
const int k = *prev(b) + i;
res += (x - k + 1) / 2;
}
if (*a + i - 2 < x) { // 0 to a
const int k = *a + i - 2;
res += (k + 1) / 2;
}
return res;
};
ret[j] = pp(R[j]) - pp(L[j] - 1);
/*
const auto it = zeros.lower_bound(L[j] - i + 3);
if (it == zeros.begin()) {
ret[j] = (X[0] ^ L[j]) & 1;
} else {
const int k = *prev(it) + i - 2;
ret[j] = (max(k+1, L[j]) - k - 1) & 1;
}*/
}
if (X[0] == X[1])
zeros.erase(zeros.find(-i + 2)), st->update(-i + 2, 0);
else if (X[1] == X[2])
zeros.erase(zeros.find(-i + 3)), st->update(-i + 2, 0);
if (i == N-1)
break;
transform(i+1, 4);
if (X[2] == X[3])
zeros.insert(-i + 3), st->update(-i + 3, 1);
}
return ret;
}
