#include "fish.h"
#include <bits/stdc++.h>
#define ent '\n'

using namespace std;
typedef long long ll;
const int maxn = 1e5 + 12;

vector<int> s[maxn];
unordered_map<int, ll> dp[maxn], dpt[maxn], d[maxn];
unordered_map<int, ll> pref[maxn], mx[maxn], suff[maxn];
unordered_map<int, ll>  a[maxn], mval[maxn];

long long max_weights(int n, int m, vector<int> x, vector<int> y, vector<int> w) {
    ll ans = 0;
    for(int i=0;i<m;i++){
        x[i]++, y[i]++;
        a[x[i]][y[i]] += w[i];
        for(int d=-1;d<=1;d++){
            s[x[i] + d].push_back(y[i]);
        }
    }
    s[0] = {0};
    for(int i=1;i<=n;i++){
        s[i].push_back(0);
        sort(s[i].begin(), s[i].end());
        s[i].resize(unique(s[i].begin(), s[i].end()) - s[i].begin());
        ll sum = 0;
        for(int x:s[i]){
            sum += a[i][x];
            pref[i][x] = sum;
        }
    }
    for(int i=1;i<=n;i++){

        ll val = -1e18;

        for(int x:s[i]){
            auto it = upper_bound(s[i-1].begin(), s[i-1].end(), x) - s[i-1].begin() - 1;
            int y = s[i-1][x];
            dp[i][x] = max(mx[i-1][y] + pref[i-1][y], mval[i-1][y]);
            d[i][x] = max(dp[i][x], suff[i-1][y] - pref[i][x]);
            val = max(val, d[i][x]);
            mval[i][x] = val;
            ans = max(ans, d[i][x]);
        }

        for(auto x:s[i-1]){
            auto it = upper_bound(s[i].begin(), s[i].end(), x) - s[i].begin() - 1;
            int y = s[i][x];
            dpt[i][x] = d[i-1][x] + pref[i][y];
        }

        val = -1e18;

        for(int x:s[i]){
            auto it = upper_bound(s[i-1].begin(), s[i-1].end(), x) - s[i-1].begin();
            it--;
            int y = s[i-1][x];

            val = max(val, max(dp[i][x], dpt[i][y]) - pref[i][x]);
            mx[i][x] = val;
        }

        val = -1e18;

        if(i < n){
            for(int j=s[i].size() - 1;j>=0;j--){
                int x = s[i][j];
                auto it = upper_bound(s[i+1].begin(), s[i+1].end(), x) - s[i+1].begin() - 1;
                int y = s[i+1][it];

                val = max(val, d[i][x] + pref[i+1][y]);
                suff[i][x] = val;
            }
        }
    }
    return ans;
}