#pragma GCC optimize ("Ofast")
#include "fish.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define vi vector<int>
#define ii pair<int, int>
#define vii vector<ii>
#define tuple2 tuple<int, int>
#define tuple3 tuple<int, int, int>
const int N = 1e5;
int n, m;
vi c[N];
unordered_map<int, int> w[N];
unordered_map<int, ll> pre[N];
unordered_map<int, ll> dp[4][N];
ll mx(int curr, int h1, int state) {
if (curr == -1) return 0;
auto it = dp[state][curr].find(h1);
if (it != dp[state][curr].end()) return it->second;
if (state != 3) dp[state][curr][h1] = mx(curr-1, h1, 3);
else dp[state][curr][h1] = mx(curr-1, 0, 2);
it = dp[state][curr].find(h1);
if (!state) {
if (curr+1 < n) {
for (int h : c[curr+1]) {
h++;
if (h >= h1) break;
ll cnt = 0;
// ver si pillo los de la izquierda
if (curr-1 >= 0) {
cnt += pre[curr-1][h-1];
}
// ver si he eliminado alguno de los que he pillado
cnt -= pre[curr][min(h, h1)-1];
it->second = max(it->second, cnt + mx(curr-1, h, 0));
}
}
if (curr-1 >= 0) {
for (int h : c[curr-1]) {
h++;
if (h >= h1) break;
ll cnt = 0;
// ver si pillo los de la izquierda
if (curr-1 >= 0) {
cnt += pre[curr-1][h-1];
}
// ver si he eliminado alguno de los que he pillado
cnt -= pre[curr][min(h, h1)-1];
it->second = max(it->second, cnt + mx(curr-1, h, 0));
}
}
}
else if (state == 1 || state == 2) {
if (curr+1 < n) {
for (int h : c[curr+1]) {
h++;
ll cnt = 0;
// ver si pillo los de la izquierda
if (curr-1 >= 0) {
cnt += pre[curr-1][h-1];
}
// ver si pillo los de la derecha
if (h > h1 && curr+1 < n) {
cnt += pre[curr+1][h-1] - pre[curr+1][h1-1];
}
// ver si he eliminado alguno de los que he pillado
cnt -= pre[curr][min(h, h1)-1];
if (h <= h1) it->second = max(it->second, cnt + mx(curr-1, h, 0));
else it->second = max(it->second, cnt + mx(curr-1, h, 1));
}
}
if (curr-1 >= 0) {
for (int h : c[curr-1]) {
h++;
ll cnt = 0;
// ver si pillo los de la izquierda
if (curr-1 >= 0) {
cnt += pre[curr-1][h-1];
}
// ver si pillo los de la derecha
if (h > h1 && curr+1 < n) {
cnt += pre[curr+1][h-1] - pre[curr+1][h1-1];
}
// ver si he eliminado alguno de los que he pillado
cnt -= pre[curr][min(h, h1)-1];
if (h <= h1) it->second = max(it->second, cnt + mx(curr-1, h, 0));
else it->second = max(it->second, cnt + mx(curr-1, h, 1));
}
}
}
else {
if (curr+1 < n) {
for (int h : c[curr+1]) {
h++;
ll cnt = 0;
// ver si pillo los de la izquierda
if (curr-1 >= 0) {
cnt += pre[curr-1][h-1];
}
// ver si pillo los de la derecha
if (h > h1 && curr+1 < n) {
cnt += pre[curr+1][h-1] - pre[curr+1][h1-1];
}
it->second = max(it->second, cnt + mx(curr-1, h, 2));
}
}
if (curr-1 >= 0) {
for (int h : c[curr-1]) {
h++;
ll cnt = 0;
// ver si pillo los de la izquierda
if (curr-1 >= 0) {
cnt += pre[curr-1][h-1];
}
// ver si pillo los de la derecha
if (h > h1 && curr+1 < n) {
cnt += pre[curr+1][h-1] - pre[curr+1][h1-1];
}
it->second = max(it->second, cnt + mx(curr-1, h, 2));
}
}
}
return it->second;
}
long long max_weights(int N, int M, std::vector<int> X, std::vector<int> Y,
std::vector<int> W) {
n = N;
m = M;
ll sum = 0;
bool odd = 0;
int mxX = 0;
for (int i = 0; i < m; i++) {
sum += W[i];
if (X[i]%2) odd = 1;
mxX = max(mxX, X[i]);
w[X[i]][Y[i]] = W[i];
c[X[i]].push_back(Y[i]);
}
if (!odd) return sum;
if (mxX <= 1) {
ll pre0[n], pre1[n];
for (int i = 0; i < n; i++) {
pre0[i] = (i ? pre0[i-1] : 0);
pre1[i] = (i ? pre1[i-1] : 0);
auto it = w[0].find(i);
if (it != w[0].end()) pre0[i] += it->second;
it = w[1].find(i);
if (it != w[1].end()) pre1[i] += it->second;
}
if (n == 2) return max(pre0[n-1], pre1[n-1]);
ll ans = max(pre0[n-1], pre1[n-1]);
for (int i = 0; i < n; i++) {
ans = max(ans, pre0[i] + pre1[n-1] - pre1[i]);
}
if (n >= 3) return ans;
}
map<int, int> heights;
for (int i = 0; i < n; i++) {
pre[i][-1] = 0;
for (int &h : c[i]) heights[h]++;
if (i >= 3) {
for (int &h : c[i-3]) {
heights[h]--;
if (!heights[h]) heights.erase(h);
}
}
ll sum1 = 0;
ll sum2 = 0;
ll sum3 = 0;
for (auto &[h, cnt] : heights) {
auto it = w[i].find(h);
if (it != w[i].end()) sum3 += it->second;
pre[i][h] = sum3;
if (i-1 >= 0) {
it = w[i-1].find(h);
if (it != w[i-1].end()) sum2 += it->second;
pre[i-1][h] = sum2;
}
if (i-2 >= 0) {
it = w[i-2].find(h);
if (it != w[i-2].end()) sum1 += it->second;
pre[i-2][h] = sum1;
}
}
}
return mx(n-1, 0, 2);
}
