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;
using ll = long long;
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx,bmi,bmi2,lzcnt,popcnt")
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]++;
map<int, int> mp[N+5];
for(int i=0; i<M; i++) mp[X[i]][Y[i]] = W[i];
ll ans = 0;
vector<pair<int, int> > vec[N+5];
vector<int> pos[N+5], SZ(N+5);
for(int i=1; i<=N; i++) vec[i].push_back({ 0, 0 });
for(int i=0; i<M; i++) vec[X[i]].push_back({ Y[i], W[i] });
for(int i=1; i<=N; i++) {
set<int> st;
for(auto &x : vec[i-1]) st.insert(x.first);
for(auto &x : vec[i]) st.insert(x.first);
for(auto &x : vec[i+1]) st.insert(x.first);
for(auto &x : st) pos[i].push_back(x);
sort(vec[i].begin(), vec[i].end());
// cout << i << ": ";
// for(int &x : pos[i]) cout << x << " ";
// cout << '\n';
}
vector<vector<ll> > pref(N+5);
vector<vector<vector<ll> > > dp(N+5);
for(int i=1; i<=N; i++) {
SZ[i] = pos[i].size() - 1;
pref[i].resize(SZ[i] + 5);
dp[i].resize(SZ[i] + 5, vector<ll>(2));
for(int j=1; j<=SZ[i]; j++) pref[i][j] = pref[i][j-1] + mp[i][pos[i][j]];
// cout << i << ": ";
// for(ll &x : pref[i]) cout << x << " ";
// cout << '\n';
}
for(int i=2; i<=N; i++) {
for(int j=0; j<=SZ[i]; j++) {
// cout << i << " " << pos[i][j] << '\n';
for(int k=0; k<=SZ[i-1]; k++) {
if(pos[i][j] >= pos[i-1][k]) {
int p = upper_bound(pos[i-1].begin(), pos[i-1].end(), pos[i][j]) - pos[i-1].begin() - 1;
dp[i][j][1] = max(dp[i][j][1], dp[i-1][k][1] + pref[i-1][p] - pref[i-1][k]);
}
if(pos[i][j] <= pos[i-1][k]) {
int p = upper_bound(pos[i].begin(), pos[i].end(), pos[i-1][k]) - pos[i].begin() - 1;
dp[i][j][0] = max(dp[i][j][0], max(dp[i-1][k][0], dp[i-1][k][1]) + pref[i][p] - pref[i][j]);
}
}
if(i < 3) continue;
for(int k=0; k<=SZ[i-2]; k++) {
int p1 = upper_bound(pos[i-1].begin(), pos[i-1].end(), pos[i][j]) - pos[i-1].begin() - 1;
int p2 = upper_bound(pos[i-1].begin(), pos[i-1].end(), pos[i-2][k]) - pos[i-1].begin() - 1;
dp[i][j][0] = max(dp[i][j][0], max(dp[i-2][k][0], dp[i-2][k][1]) + max((p1 > -1 ? pref[i-1][p1] : 0), (p2 > -1 ? pref[i-1][p2] : 0)));
dp[i][j][1] = max(dp[i][j][1], max(dp[i-2][k][0], dp[i-2][k][1]) + max((p1 > -1 ? pref[i-1][p1] : 0), (p2 > -1 ? pref[i-1][p2] : 0)));
}
}
}
for(int i=1; i<=N; i++) {
for(int j=0; j<=SZ[i]; j++) {
if(pref[i+1].empty() || j == 0) ans = max({ ans, dp[i][j][0], dp[i][j][1] });
else {
int p = upper_bound(pos[i+1].begin(), pos[i+1].end(), pos[i][j]) - pos[i+1].begin() - 1;
ans = max(ans, max(dp[i][j][0], dp[i][j][1]) + pref[i+1][p]);
}
}
}
return ans;
}
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