#include "fish.h"
#pragma GCC target ("avx2")
#pragma GCC optimize ("O3")
#pragma GCC optimize ("unroll-loops")
#include<bits/stdc++.h>
#include<math.h>
using namespace std;
typedef long long int ll;
typedef long double ld;
typedef pair<ll, ll> pl;
typedef vector<ll> vl;
#define FD(i, r, l) for(ll i = r; i > (l); --i)
#define K first
#define V second
#define G(x) ll x; cin >> x;
#define GD(x) ld x; cin >> x;
#define GS(s) string s; cin >> s;
#define EX(x) { cout << x << '\n'; exit(0); }
#define A(a) (a).begin(), (a).end()
#define F(i, l, r) for (ll i = l; i < (r); ++i)
#define NN 310
ll grid[NN][NN];
ll n;
ll dp1[NN][NN];
ll noreq(ll, ll); // no request fishies, so len == prev wall.
ll dp2[NN][NN];
ll req(ll, ll);
// previous column did NOT request any right fishies here
// so we simply have a free wall to attach to
ll noreq(ll i, ll len) {
// assert(len == 0 or len == n);
if (i == n) return 0;
auto &DP = dp1[i][len];
if (!~DP) {
DP = noreq(i+1, n); // no restrictions so build big wall.
F(nlen, 0, n+1) DP = max(DP, req(i, nlen)); // basically can set up any wall here before taking right fishes
ll lsum = 0;
F(j, 0, len) {
lsum += grid[i][j];
}
DP = max(DP, lsum + noreq(i+1, 0));
{
ll tsum = lsum;
F(j, 0, len) {
tsum -= grid[i][j];
DP = max(DP, tsum + noreq(i+1, j+1));
}
}
F(covering, len, n) {
// not lsum naymore jsut cum sum
lsum += grid[i][covering];
DP = max(DP, lsum + req(i+1, covering + 1));
}
}
return DP;
}
// previous column requested right fishes here;
// so len == min bound on wall (we cannot take anything below len)
ll req(ll i, ll len) {
if (i == n) return len == 0 ? 0 : -9e18; // i should need 0 fishes here
auto &DP = dp2[i][len];
if (!~DP) {
// note that we cannot request any left fishes here.
DP = noreq(i+1, n); // if we don't request ANY fish here, just go up to max
ll sm = 0;
F(covering, len, n) {
sm += grid[i][covering];
DP = max(DP, sm + req(i+1, covering + 1));
}
}
return DP;
}
long long max_weights(int N, int M, std::vector<int> X, std::vector<int> Y,
std::vector<int> W) {
ll rans;
if (N <= 300) {
memset(dp1, -1, sizeof dp1);
memset(dp2, -1, sizeof dp2);
n = N;
memset(grid, 0, sizeof grid);
F(i, 0, M) grid[X[i]][Y[i]] = W[i];
rans = noreq(0, 0);
}
constexpr ll DEBUG = 01;
if (N <= 300 and !DEBUG) return rans;
bool case1 = 1;
bool case2 = 1;
bool case3 = 1;
F(i, 0, M) case1 &= X[i]%2 == 0;
F(i, 0, M) case2 &= X[i] <= 1;
F(i, 0, M) case3 &= Y[i] == 0;
if (case1) {
return accumulate(A(W), 0ll);
} else if (case2) {
ll c[2] = {};
map<pl, ll> points;
F(i, 0, M) {
c[X[i]] += W[i];
points[{X[i], Y[i]}] = W[i];
}
if (N == 2) {
return max(c[0], c[1]);
}
ll tans = max(c[0], c[1]);
ll tsum = c[1];
F(i, 0, N) {
tsum -= points[{1, i}];
tsum += points[{0, i}];
tans = max(tans, tsum);
}
return tans;
} else if (case3) {
vl grid(n);
F(i, 0, M) grid[X[i]] = W[i];
vector<vl> dp(n+10, vl(3, -1));
auto rec = [&](auto &&self, ll i, ll f) -> ll {
if (i > n) return -1e18;
if (i >= n) return 0;
auto &DP = dp[i][f];
if (!~DP) {
DP = self(self, i+1, 1);
if (f) DP = max(DP, grid[i] + self(self, i+1, 0));
DP = max(DP, grid[i] + self(self, i+2, 1));
}
return DP;
};
// cout << rec(rec, 0, 0) << ' ' << rans << endl;
// assert(rec(rec, 0, 0) == rans);
return rec(rec, 0, 0);
}
return -1;
}
