#include "wombats.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> pll;
#define X first
#define Y second
#define sep ' '
#define debug(x) cerr << #x << ": " << x << endl;
const ll MAXN = 5000 + 10;
const ll MAXM = 200 + 10;
const ll INF = 1e9 + 10;
const ll LIM = 5;
int n, m, H[MAXN][MAXM], V[MAXN][MAXM], ps[MAXN][MAXM], sg[MAXN][MAXM][MAXM], opt[MAXM][MAXM],
lc[MAXN << 1], rc[MAXN << 1], sgsz = 1, dist[MAXN][MAXM];
inline void update_ps(int i) {
for (int j = 2; j <= m; j++)
ps[i][j] = ps[i][j - 1] + H[i][j - 1];
}
inline void update_ans(int mid, int v) { // opt[i - 1][j] <= opt[i][j] <= opt[i][j + 1]
for (int i = 1; i <= m; i++) {
opt[i][m + 1] = m;
opt[0][i] = 1;
}
for (int i = 1; i <= m; i++) {
for (int j = m; j > 0; j--) {
int optl = opt[i - 1][j], optr = opt[i][j + 1];
sg[v][i][j] = INF;
opt[i][j] = optl;
for (int t = optl; t <= optr; t++) {
int cost = sg[lc[v]][i][t] + V[mid][t] + sg[rc[v]][t][j];
if (cost < sg[v][i][j]) {
sg[v][i][j] = cost;
opt[i][j] = t;
}
}
}
}
}
inline void dijkstra(int x, int y, int r) {
priority_queue<pair<ll, pll>, vector<pair<ll, pll>>, greater<pair<ll, pll>>> pq;
for (int i = x; i <= r; i++)
for (int j = 1; j <= m; j++)
dist[i][j] = INF;
dist[x][y] = 0;
pq.push({dist[x][y], {x, y}});
while (!pq.empty()) {
auto [d, pos] = pq.top();
pq.pop();
auto [x, y] = pos;
if (dist[x][y] != d) continue;
if (x < r && dist[x + 1][y] > dist[x][y] + V[x][y]) {
dist[x + 1][y] = dist[x][y] + V[x][y];
pq.push({dist[x + 1][y], {x + 1, y}});
}
if (y > 1 && dist[x][y - 1] > dist[x][y] + H[x][y - 1]) {
dist[x][y - 1] = dist[x][y] + H[x][y - 1];
pq.push({dist[x][y - 1], {x, y - 1}});
}
if (y < m && dist[x][y + 1] > dist[x][y] + H[x][y]) {
dist[x][y + 1] = dist[x][y] + H[x][y];
pq.push({dist[x][y + 1], {x, y + 1}});
}
}
}
inline void tof(int l, int r, int v) {
for (int i = 1; i <= m; i++) {
dijkstra(l, i, r);
for (int j = 1; j <= m; j++)
sg[v][i][j] = dist[r][j];
}
}
void build(int l = 1, int r = n, int v = 1) {
if (r - l + 1 <= LIM) {
tof(l, r, v);
} else {
int mid = (l + r) >> 1;
lc[v] = ++sgsz;
rc[v] = ++sgsz;
build(l, mid, lc[v]);
build(mid + 1, r, rc[v]);
update_ans(mid, v);
}
}
void update(int ind, int l = 1, int r = n, int v = 1) {
if (r - l + 1 <= LIM) {
tof(l, r, v);
} else {
int mid = (l + r) >> 1;
if (ind <= mid) update(ind, l, mid, lc[v]);
else update(ind, mid + 1, r, rc[v]);
update_ans(mid, v);
}
}
void init(int R_, int C_, int H_[5000][200], int V_[5000][200]) {
n = R_, m = C_;
for (int i = 1; i <= n; i++)
for (int j = 1; j < m; j++)
H[i][j] = H_[i - 1][j - 1];
for (int i = 1; i < n; i++)
for (int j = 1; j <= m; j++)
V[i][j] = V_[i - 1][j - 1];
for (int i = 1; i <= n; i++)
update_ps(i);
build();
}
void changeH(int P, int Q, int W) {
P++, Q++;
H[P][Q] = W;
update_ps(P);
update(P);
}
void changeV(int P, int Q, int W) {
P++, Q++;
V[P][Q] = W;
update(P);
}
int escape(int V1, int V2) {
V1++, V2++;
return sg[1][V1][V2];
}
// TODO: 1-base
// TODO: check fit in ll
// TODO: change max limits
// TODO: check n == 1
// TODO: check bounds(n / m)
