// 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 ZCK {
struct VAL {
int val, cnt;
VAL(int v = 0, int c = 1): val(v), cnt(c) {}
VAL operator+ (int v) { return VAL(val + v, cnt); }
VAL operator+ (VAL v) {
if(val < v.val) return *this;
if(val > v.val) return v;
return VAL(val, cnt + v.cnt);
}
};
struct NOD {
VAL val; int tag;
NOD (int v = 0): val(v), tag(0) {}
VAL get() { return val + tag; }
};
int n; vector<NOD> nds;
void init(int nn){
n = nn; nds.resize(n * 2);
for(int i = 0; i < n; ++i) nds[i + n] = NOD(pre[i]);
for(int i = n-1; i > 0; --i) nds[i].val = nds[i<<1].get() + nds[i<<1|1].get();
}
void pull(int p){ for(p >>= 1; p > 0; p >>= 1) nds[p].val = nds[p<<1].get() + nds[p<<1|1].get(); }
void mod(int l, int r, int v){
int tl = l + n, tr = r + n - 1;
for(l += n, r += n; l < r; l >>= 1, r >>= 1){
if(l & 1) nds[l++].tag += v;
if(r & 1) nds[--r].tag += v;
}
pull(tl), pull(tr);
}
int que(){ return nds[1].get().cnt; }
} 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, 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];
sgt.init(H * W);
bld = false;
}
int swap_seats(int a, int 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();
}
