This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include "fish.h"
#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
#ifndef EVAL
#include "grader.cpp"
#endif
const int N = 3005;
vector<ll> dp[N], id[N];
ll P[N][N], sz[N], tmp[N][N], pre[N];
ll pref[N][N], suff[N][N], mx[N][N];
ll max_weights(int n, int m, vector<int> x, vector<int> y, vector<int> w) {
for(int i=0;i<m;i++){
x[i]++, y[i]++;
if(x[i] > 1) dp[x[i] - 1].push_back(y[i]);
if(x[i] < n) dp[x[i] + 1].push_back(y[i]);
dp[x[i]].push_back(y[i]);
P[x[i]][y[i]] += w[i];
}
for(int i=1;i<=n;i++){
for(int j=1;j<=n;j++){
P[i][j] += P[i][j-1];
}
}
for(int i=0;i<N;i++){
swap(id[i], dp[i]);
id[i].push_back(0);
sort(id[i].begin(), id[i].end());
id[i].erase(unique(id[i].begin(), id[i].end()), id[i].end());
dp[i].resize(id[i].size());
}
sz[0] = 1;
for(int i=1;i<=n;i++){
int j_ = 0;
for(auto j : id[i]){
int pos, p2;
if(i > 1){
pos = lower_bound(id[i-2].begin(), id[i-2].end(), j) - id[i-2].begin();
p2 = upper_bound(id[i-2].begin(), id[i-2].end(), j) - id[i-2].begin();
} else {
pos = 0;
p2 = 1;
}
int k_ = 0;
for(auto k : id[i-1]){
tmp[j_][k_] = 0;
if(j <= k){
tmp[j_][k_] = max(tmp[j_][k_], pref[k_][sz[i-1] - 1] + P[i-1][j] + P[i+1][j] - (i > 1 ? P[i][j] : 0) - P[i-1][j]);
} else {
tmp[j_][k_] = max(tmp[j_][k_], pref[k_][pre[k_] - 1] + P[i-1][j] + P[i+1][j] - (i > 1 ? P[i][k] : 0) - P[i-1][k]);
if(pos < sz[i-1]) tmp[j_][k_] = max(tmp[j_][k_], suff[k_][pos] + P[i-1][j] + P[i+1][j] - (i > 1 ? P[i][k] : 0) - P[i-1][j]);
if(p2) tmp[j_][k_] = max(tmp[j_][k_], mx[k_][p2 - 1] + P[i-1][j] + P[i+1][j] - (i > 1 ? P[i][k] : 0));
}
k_++;
}
j_++;
}
sz[i] = id[i-1].size();
for(int j=0;j<(int)id[i].size();j++){
suff[j][sz[i]] = 0;
for(int k=0;k<sz[i];k++){
pref[j][k] = suff[j][k] = mx[j][k] = tmp[j][k];
mx[j][k] -= P[i][id[i-1][k]];
}
for(int k=1;k<sz[i];k++){
pref[j][k] = max(pref[j][k], pref[j][k - 1]);
}
for(int k=sz[i]-1;k>=0;k--){
suff[j][k] = max(suff[j][k+1], suff[j][k]);
}
pre[j] = lower_bound(id[i - 1].begin(), id[i - 1].end(), id[i][j]) - id[i - 1].begin();
for(int k=pre[j] + 1;k<sz[i];k++){
mx[j][k] = max(mx[j][k-1], mx[j][k]);
}
pre[j] = upper_bound(id[i - 1].begin(), id[i - 1].end(), id[i][j]) - id[i - 1].begin();
}
}
ll res = 0;
for(int i=0;i<=n;i++){
for(int j=0;j<=n;j++){
res = max(res, tmp[i][j]);
}
}
return res;
}
/*
5 4
0 2 5
1 1 2
4 4 1
3 3 3
5 6
2 3 3
2 1 2
4 1 3
2 0 10
4 4 1
4 0 7
*/
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