#include "seats.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int, int>;
ll h, w;
vector<vector<ll>> grid, prefixGrid;
vector<pii> pos;
bool outOfBounds(pii coords)
{
int i = coords.first, j = coords.second;
return i < 0 || i >= h || j < 0 || j >= w;
}
void calcPrefix()
{
for (int i = 0; i < h; i++)
for (int j = 0; j < w; j++)
{
pii above = {i - 1, j};
pii before = {i, j - 1};
pii upLeft = {i - 1, j - 1};
ll res = grid[i][j];
if (!outOfBounds(above))
res += prefixGrid[above.first][above.second];
if (!outOfBounds(before))
res += prefixGrid[before.first][before.second];
if (!outOfBounds(upLeft))
res -= prefixGrid[upLeft.first][upLeft.second];
prefixGrid[i][j] = res;
}
}
ll getArea(pii tL, pii bR)
{
return (bR.first - tL.first + 1) * (bR.second - tL.second + 1);
}
ll getRectangleSum(pii topLeftCorner, pii bottomRightCorner)
{
pii before = {bottomRightCorner.first, topLeftCorner.second - 1};
pii above = {topLeftCorner.first - 1, bottomRightCorner.second};
pii upLeft = {topLeftCorner.first - 1, topLeftCorner.second - 1};
ll res = prefixGrid[bottomRightCorner.first][bottomRightCorner.second];
if (!outOfBounds(above))
res -= prefixGrid[above.first][above.second];
if (!outOfBounds(before))
res -= prefixGrid[before.first][before.second];
if (!outOfBounds(upLeft))
res += prefixGrid[upLeft.first][upLeft.second];
return res;
}
ll checkBeauty()
{
ll res = 0;
int top = 0;
pair<ll, ll> prevTL = {-1, -1}, prevBR = {-1, -1};
pair<ll, ll> topLeft = pos[0], bottomRight = pos[0];
do
{
ll area = getArea(topLeft, bottomRight);
bool isPretty = getRectangleSum(topLeft, bottomRight) == area * (area - 1) / 2;
top++;
res += isPretty && (topLeft != prevTL || bottomRight != prevBR);
prevTL = topLeft;
prevBR = bottomRight;
pii posNext = pos[top];
topLeft.first = min(topLeft.first, (ll)posNext.first);
topLeft.second = min(topLeft.second, (ll)posNext.second);
bottomRight.first = max(bottomRight.first, (ll)posNext.first);
bottomRight.second = max(bottomRight.second, (ll)posNext.second);
} while (top < h * w);
return res;
}
void give_initial_chart(int H, int W, std::vector<int> R, std::vector<int> C)
{
h = H, w = W;
grid = prefixGrid = vector<vector<ll>>(H, vector<ll>(W));
pos = vector<pair<int, int>>(H * W);
for (int i = 0; i < H * W; i++)
{
grid[R[i]][C[i]] = i;
pos[i] = {R[i], C[i]};
}
}
int swap_seats(int a, int b)
{
pair<int, int> aPos = pos[a], bPos = pos[b];
swap(grid[aPos.first][aPos.second], grid[bPos.first][bPos.second]);
swap(pos[a], pos[b]);
calcPrefix();
return checkBeauty();
}
