#include "fish.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int maxn = 1e5 + 10, smalln = 3010;
vector < pair < int, int > > col[maxn];
vector < int > state[maxn];
unordered_set < int > state_set[maxn];
vector < vector < ll > > dp[maxn];
vector < ll > pref[maxn];
ll get_sum(int j, int left, int right)
{
if (left > right)
return 0;
int lf = 0, rf = (int)(col[j].size()) - 1;
while(lf <= rf)
{
int mf = (lf + rf) / 2;
if (col[j][mf].first >= left)
rf = mf - 1;
else
lf = mf + 1;
}
int lb = rf;
lf = 0;
rf = (int)(col[j].size()) - 1;
while(lf <= rf)
{
int mf = (lf + rf) / 2;
///cout << col[j][mf].second << endl;
if (col[j][mf].first <= right)
lf = mf + 1;
else
rf = mf - 1;
}
int rb = rf;
/// cout << lb << " " << rb << " " << j << " " << left << " " << right << endl;
if (lb >= rb || rb < 0)
return 0;
ll sum = pref[j][rb];
if (lb >= 0)
sum = sum - pref[j][lb];
/// cout << sum << endl;
return sum;
}
long long max_weights(int N, int M, std::vector<int> X, std::vector<int> Y,
std::vector<int> W)
{
bool all_even = true, small_x = true;
for (int i = 0; i < M; i ++)
{
if (X[i] % 2 != 0)
all_even = false;
if (X[i] > 1)
small_x = false;
}
for (int i = 0; i < M; i ++)
{
col[X[i]].push_back({Y[i], W[i]});
}
for (int i = 0; i < N; i ++)
sort(col[i].begin(), col[i].end());
for (int i = 0; i < M; i ++)
{
if (X[i] != 0)
state_set[X[i] - 1].insert(Y[i] + 1);
if (X[i] != N - 1)
state_set[X[i] + 1].insert(Y[i] + 1);
}
for (int i = 0; i < N; i ++)
{
state_set[i].insert(0);
state_set[i].insert(N);
}
for (int i = 0; i < N; i ++)
{
for (auto it : state_set[i])
state[i].push_back(it);
sort(state[i].begin(), state[i].end());
}
if (all_even)
{
ll sum = 0;
for (int i = 0; i < M; i ++)
sum = sum + W[i];
return sum;
}
else if (small_x)
{
ll zero = 0, one = 0;
for (int i = 0; i < M; i ++)
{
if (X[i] == 0)
zero += W[i];
else
one += W[i];
}
if (N == 2)
return max(zero, one);
int to = 0;
ll cur = 0, ans = 0;
for (int i = 0; i < col[0].size(); i ++)
{
if (cur + one > ans)
ans = cur + one;
cur += col[0][i].second;
while(to < col[1].size() && col[1][to].first <= col[0][i].first)
{
one -= col[1][to].second;
to ++;
}
}
if (cur + one > ans)
ans = cur + one;
return ans;
}
/**for (int i = 0; i < N; i ++, cout << endl)
for (int j = 0; j < N; j ++)
cout << val[i][j] << " ";*/
for (int i = 0; i < N; i ++)
{
pref[i].resize(col[i].size());
if (col[i].size() == 0)
continue;
pref[i][0] = col[i][0].second;
///cout << col[i][0].second << endl;
for (int j = 1; j < col[i].size(); j ++)
{
pref[i][j] = pref[i][j - 1] + col[i][j].second;
}
}
for (int i = 0; i < N; i ++)
{
dp[i].resize(state[i].size());
for (int j = 0; j < state[i].size(); j ++)
{
dp[i][j].resize(2);
}
}
for (int j = 0; j < state[1].size(); j ++)
dp[1][j][0] = dp[1][j][1] = 0;
for (int i = 1; i < N; i ++)
{
ll so_far = 0, to = 0;
for (int j = 0; j < state[i].size(); j ++)
{
if (j > 0)
dp[i][j][1] = dp[i][j - 1][1] + get_sum(i - 1, state[i][j - 1], state[i][j] - 1);
while(to < state[i - 1].size() && state[i - 1][to] <= state[i][j])
{
///cout << i << " " << j << " :: " << state[i - 1][to] << " " << state[i][j] << endl;
so_far = max(so_far, dp[i - 1][to][1] + get_sum(i - 1, state[i - 1][to], state[i][j] - 1));
to ++;
}
dp[i][j][1] = max(dp[i][j][1], so_far);
}
so_far = 0;
to = (int)(state[i - 1].size()) - 1;
for (int j = (int)(state[i].size()) - 1; j >= 0; j --)
{
if (j + 1 < state[i].size())
dp[i][j][0] = dp[i][j + 1][0] + get_sum(i, state[i][j], state[i][j + 1] - 1);
while(to >= 0 && state[i - 1][to] >= state[i][j])
{
///cout << i << " " << j << " ::: " << to << endl;
so_far = max(so_far, max(dp[i - 1][to][0], dp[i - 1][to][1]) + get_sum(i, state[i][j], state[i - 1][to] - 1));
to --;
}
dp[i][j][0] = max(dp[i][j][0], so_far);
}
if (i > 1)
{
so_far = 0;
to = 0;
for (int j = 0; j < state[i].size(); j ++)
{
while(to < state[i - 2].size() && state[i - 2][to] <= state[i][j])
{
so_far = max(so_far, max(dp[i - 2][to][0], dp[i - 2][to][1]));
to ++;
}
dp[i][j][1] = max(so_far + get_sum(i - 1, 0, state[i][j] - 1), dp[i][j][1]);
}
so_far = 0;
to = (int)(state[i - 2].size()) - 1;
for (int j = (int)(state[i].size()) - 1; j >= 0; j --)
{
while(to >= 0 && state[i - 2][to] >= state[i][j])
{
so_far = max(so_far, max(dp[i - 2][to][0], dp[i - 2][to][1]) + get_sum(i - 1, 0, state[i - 2][to] - 1));
to --;
}
dp[i][j][1] = max(so_far, dp[i][j][1]);
}
}
}
/**cout << "-----------" << endl;
for (int i = 0; i < N; i ++, cout << endl)
for (int j = 0; j < state[i].size(); j ++)
cout << dp[i][j][0] << " ";
cout << "-----------" << endl;
for (int i = 0; i < N; i ++, cout << endl)
for (int j = 0; j < state[i].size(); j ++)
cout << dp[i][j][1] << " ";*/
ll ans = 0;
for (int j = 0; j < state[N - 1].size(); j ++)
for (int t = 0; t < 2; t ++)
ans = max(ans, dp[N - 1][j][t]);
return ans;
}
