#include "fish.h"
#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef vector<ll> vi;
typedef vector<vi> vvi;
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
const ll INF = 3e5 * 1e9 + 100;
long long max_weights(int N, int M, std::vector<int> X, std::vector<int> Y, std::vector<int> W)
{
vvi grid(N + 4, vi(N, 0)); // becomes prefix grid
for (int i = 0; i < M; ++i)
grid[X[i] + 3][Y[i]] = W[i];
for (int x = 0; x < sz(grid); ++x)
for (int y = 1; y < sz(grid[0]); ++y)
grid[x][y] += grid[x][y - 1];
vvi dpg(sz(grid), vi(sz(grid[0]), 0)); // growth stack thing
vvi dp(sz(grid), vi(sz(grid[0]), 0)); // normal all dp
vi dpm(sz(grid), 0); // maximum einer Spaltes
for (int x = 3; x < sz(grid) - 1; ++x) // so i choose the borders
{
ll c1 = -INF, c2 = -INF; // running variables for case 1 and 2 // TODO: INIT
for (int y = 0; y < sz(grid[0]); ++y)
{
// Case 1 - last tower in x-1 and smaller y
c1 = max(c1, dpg[x - 1][y] - grid[x - 1][y] - grid[x][y]);
dpg[x][y] = max(dpg[x][y], grid[x - 1][y] + grid[x + 1][y] + c1);
// Case 2 - last tower in x-2 and smaller y
c2 = max(c2, dp[x - 2][y] - grid[x - 1][y]);
dpg[x][y] = max(dpg[x][y], grid[x - 1][y] + grid[x + 1][y] + c2);
// Case 3 - last tower in x-1 and larger y (or if it is smaller, case 1 performs better)
// here the last tower might be larger than the current one
dp[x][y] = max(dp[x][y], dpm[x - 1] - grid[x][y] + grid[x + 1][y]);
// Case 4 - Last Tower in x-2 and larger y (or if it is smaller, case 2 performs better)
dpg[x][y] = max(dpg[x][y], dpm[x - 2] + grid[x + 1][y]);
// Case 5 - Last Tower in x-3
dpg[x][y] = max(dpg[x][y], dpm[x - 3] + grid[x - 1][y] + grid[x + 1][y]);
// keep track for dpg & dpm
dp[x][y] = max(dp[x][y], dpg[x][y]);
dpm[x] = max(dpm[x], dp[x][y]);
}
}
return *max_element(all(dpm));
}
