// Knapsack DP is harder than FFT.
#include<bits/stdc++.h>
using namespace std;
typedef long long ll; typedef pair<int,int> pii; typedef pair<ll,ll> pll;
#define ff first
#define ss second
#define pb emplace_back
#define AI(x) begin(x),end(x)
template<class I>bool chmax(I&a,I b){return a<b?(a=b,true):false;}
template<class I>bool chmin(I&a,I b){return b<a?(a=b,true):false;}
#ifdef OWO
#define debug(args...) SDF(#args, args)
#define OIU(args...) ostream& operator<<(ostream&O,args)
#define LKJ(S,B,E,F) template<class...T>OIU(S<T...>s){O<<B;int c=0;for(auto i:s)O<<(c++?", ":"")<<F;return O<<E;}
LKJ(vector,'[',']',i)LKJ(deque,'[',']',i)LKJ(set,'{','}',i)LKJ(multiset,'{','}',i)LKJ(unordered_set,'{','}',i)LKJ(map,'{','}',i.ff<<':'<<i.ss)LKJ(unordered_map,'{','}',i.ff<<':'<<i.ss)
template<class...T>void SDF(const char* s,T...a){int c=sizeof...(T);if(!c){cerr<<"\033[1;32mvoid\033[0m\n";return;}(cerr<<"\033[1;32m("<<s<<") = (",...,(cerr<<a<<(--c?", ":")\033[0m\n")));}
template<class T,size_t N>OIU(array<T,N>a){return O<<vector<T>(AI(a));}template<class...T>OIU(pair<T...>p){return O<<'('<<p.ff<<','<<p.ss<<')';}template<class...T>OIU(tuple<T...>t){return O<<'(',apply([&O](T...s){int c=0;(...,(O<<(c++?", ":"")<<s));},t),O<<')';}
#else
#pragma GCC optimize("Ofast")
#define debug(...) ((void)0)
#endif
#include "seats.h"
int H, W;
vector<int> R, C;
vector<vector<int>> A;
vector<int> pre;
bool bld;
struct SGT {
struct NOD {
int val, cnt, tag;
NOD(): val(0), cnt(0), tag(0) {}
NOD(int v): val(v), cnt(1), tag(0) {}
NOD(int v, int c, int t): val(v), cnt(c), tag(t) {}
};
int n; vector<NOD> nds;
void mer(NOD &u, NOD a, NOD b) {
if(a.val > b.val) swap(a, b);
u = NOD(a.val, a.cnt, 0);
if(u.val == b.val) u.cnt += b.cnt;
}
void upd(NOD &u, int t){ u.val += t, u.tag += t; }
void init(int l, int r, int i){
if(l == r){ nds[i] = NOD(pre[l]); return; }
int m = (l + r) / 2;
init(l, m, i*2); init(m + 1, r, i*2+1);
mer(nds[i], nds[i*2], nds[i*2+1]);
}
void init(int nn) {
n = nn - 1; nds.resize(n * 4 + 1);
init(0, n, 1);
}
void mod(int l, int r, int i, int ql, int qr, int v) {
if(ql <= l and r <= qr){ upd(nds[i], v); return; }
int m = (l + r) / 2;
NOD &u = nds[i], &a = nds[i * 2], &b = nds[i*2+1];
upd(a, u.tag), upd(b, u.tag), u.tag = 0;
if(ql <= m) mod(l, m, i*2, ql, qr, v);
if(m+1 <= qr) mod(m+1, r, i*2+1, ql, qr, v);
mer(u, a, b);
}
void mod(int ql, int qr, int v) { mod(0, n, 1, ql, qr, v); }
int que() { return nds[1].cnt; }
void de(int l, int r, int i){
NOD &u = nds[i];
debug(l, r, u.val, u.cnt, u.tag);
if(l == r) return;
int m = (l + r) / 2;
de(l, m, i*2);
de(m+1, r, i*2+1);
}
void de(){ de(0, n, 1); }
} sgt;
inline int eek(int i, int j){ return (i < 0 or j < 0 or i >= H or j >= W ? H * W : A[i][j]); }
void add(int l, int r, int v){
if(l == r) return;
if(bld) pre[l] += v, pre[r] -= v;
else sgt.mod(l, r-1, v);
}
void upd(int i, int j, int v){
vector<int> tmp({ eek(i, j), eek(i-1, j), eek(i, j-1), eek(i-1, j-1) });
sort(AI(tmp));
add(tmp[0], tmp[1], v);
add(tmp[2], tmp[3], v);
}
void give_initial_chart(int H, int W, vector<int> R, vector<int> C) {
::H = H, ::W = W;
::R = R, ::C = C;
A.assign(H, vector<int>(W, 0));
for(int i = 0; i < H * W; ++i) A[R[i]][C[i]] = i;
pre.assign(H * W + 1, 0); bld = true;
for(int i = 0; i <= H; ++i) for(int j = 0; j <= W; ++j) upd(i, j, 1);
for(int i = 1; i <= H * W; ++i) pre[i] += pre[i-1];
debug(pre);
sgt.init(H * W);
sgt.de();
bld = false;
}
int swap_seats(int a, int b) {
debug(a, b);
for(int d: {0, 1}) for(int e: {0, 1}) upd(R[a] + d, C[a] + e, -1);
for(int d: {0, 1}) for(int e: {0, 1}) upd(R[b] + d, C[b] + e, -1);
swap(A[R[a]][C[a]], A[R[b]][C[b]]);
swap(R[a], R[b]), swap(C[a], C[b]);
for(int d: {0, 1}) for(int e: {0, 1}) upd(R[a] + d, C[a] + e, 1);
for(int d: {0, 1}) for(int e: {0, 1}) upd(R[b] + d, C[b] + e, 1);
return sgt.que();
}
