#include "fish.h"
#include<bits/stdc++.h>
#define pb push_back
#include <vector>
using namespace std;
const int maxn = 3005;
int n, m;
vector < pair < int, int > > g[200000];
long long dp[maxn][maxn][10];
long long best[maxn];
long long pref[maxn][maxn], a[maxn][maxn];
long long get(int col, int l, int r)
{
if(r < l)return 0;
if(col > n)return 0;
long long val = pref[col][r];
if(l)val -= pref[col][l-1];
return val;
}
long long p[4][200000];
long long get_p(long long col, long long l, long long r)
{
if(r < l)return 0;
if(col > n)return 0;
long long val = p[col][r];
if(l)val -= p[col][l-1];
return val;
}
long long val[200000], d[200000][2][2];
long long max_weights(int N, int M, std::vector<int> X, std::vector<int> Y,
std::vector<int> W) {
n = N;
m = M;
long long sum = 0, group1 = 1, group2 = 1, group3 = 1;
for (int i = 0; i < m; ++ i)
{
if(X[i] % 2 == 1)group1 = 0;
if(X[i] > 1)group2 = 0;
if(Y[i] > 0)group3 = 0;
X[i] ++;
Y[i] ++;
g[X[i]].pb(make_pair(Y[i], W[i]));
sum += W[i];
if(n <= 3000)a[X[i]][Y[i]] = W[i];
if(X[i] <= 2)p[X[i]][Y[i]] += W[i];
if(Y[i] == 1)val[X[i]] += W[i];
}
if(group1)return sum;
if(group2)
{
long long sum1 = 0, sum2 = 0;
for (auto &[y, w]: g[1])
sum1 += w;
for (auto &[y, w]: g[2])
sum2 += w;
long long ans = max(sum1, sum2);
if(n > 2)
{
for (int i = 1; i <= 2; ++ i)
{
for (int j = 1; j <= n; ++ j)
p[i][j] += p[i][j-1];
}
for (int i = 0; i <= n; ++ i)
{
long long curr = get_p(1, 1, i) + get_p(2, i+1, n);
ans = max(ans, curr);
}
}
return ans;
}
if(group3)
{
d[1][0][0] = 0;
d[1][0][1] = 0;
long long ans = 0;
if(n > 1)ans = val[2];
for (int i = 2; i <= n; ++ i)
{
/// 0
d[i][0][0] = max(d[i-1][0][0], d[i-1][1][0]);
d[i][1][0] = max(d[i-1][0][1], d[i-1][1][1]) + val[i];
/// 1
d[i][0][1] = max(d[i-1][0][0] + val[i-1], d[i-1][1][0]);
d[i][1][1] = max(d[i-1][0][1], d[i-1][1][1]);
ans = max(ans, max(d[i][0][1], d[i][1][1]) + val[i+1]);
}
return ans;
}
for (int i = 0; i <= n; ++ i)
{
pref[i][0] = a[i][0];
for (int j = 1; j <= n; ++ j)
pref[i][j] = pref[i][j-1] + a[i][j];
}
long long ans = 0;
for (int j = 0; j <= n; ++ j)
{
if(n >= 2)
{
ans = max(ans, get(2, 1, j));
best[1] = ans;
}
}
for (int i = 2; i <= n; ++ i)
{
dp[i][0][0] = best[i-1];
dp[i][0][1] = best[i-1];
for (int j = 1; j <= n; ++ j)
{
// cout << "solving " << i << " " << j << endl;
for (int pre = 1; pre <= j; ++ pre)
{
dp[i][j][0] = max(dp[i][j][0], dp[i-1][pre][0] + get(i-1, pre + 1, j));
}
for (int pre = j; pre <= n; ++ pre)
{
dp[i][j][1] = max(dp[i][j][1], dp[i-1][pre][1] + get(i, j+1, pre));
}
// cout << "after basic cases" << dp[i][j][0] << " " << dp[i][j][1] << endl;
/// start new
for (int pre = 1; pre <= n; ++ pre)
{
if(i > 2)
{
long long curr = max(dp[i-2][pre][0], dp[i-2][pre][1]) + get(i-1, 1, max(pre, j));
dp[i][j][0] = max(dp[i][j][0], curr);
dp[i][j][1] = max(dp[i][j][1], curr);
}
//if(curr == 801326851508)return 0/0;
}
long long curr = get(i-1, 1, j);
if(i >= 3)curr += best[i-3];
dp[i][j][0] = max(dp[i][j][0], curr);
dp[i][j][1] = max(dp[i][j][1], curr);
if(curr == 801326851508)return 0/0;
// cout << "after " << dp[i][j][0] << " " << dp[i][j][1] << endl;
ans = max(ans, max(dp[i][j][0], dp[i][j][1]) + get(i+1, 1, j));
}
best[i] = ans;
}
return ans;
}
