#include <bits/stdc++.h>
using namespace std;
#define ll long long
constexpr int MAXN = 1e5 + 5;
constexpr int PW = 512;
ll sum_tutto(int N, int M, vector<int> X, vector<int> Y, vector<int> W) {
ll sum = 0;
for (auto x : W) sum += x;
return sum;
}
ll res_minore_di_due(int N, int M, vector<int> X, vector<int> Y, vector<int> W) {
if (N == 2) {
// massimo tra 0 e 1
ll one = 0;
ll zero = 0;
for (int i = 0; i < M; i ++) {
if (X[i] == 0) zero += W[i];
else one += W[i];
}
return max(one, zero);
}
// altrimenti piazza una riga in 2 e poi prendi prefisso maggiore piazzando in 1
ll sum = 0;
for (int i = 0; i < M; i ++) {
if (X[i] == 1) sum += W[i];
}
vector<vector<ll>> pos(2, vector<ll>(N + 5, 0));
for (int i = 0; i < M; i ++) {
pos[X[i]][Y[i]] += W[i];
}
ll best_res = sum;
ll sum_zero = 0;
ll sum_uno = 0;
for (int i = 0; i < N + 5; i ++) {
sum_zero += pos[0][i];
sum_uno += pos[1][i];
best_res = max(best_res, sum - sum_uno + sum_zero);
}
return best_res;
}
ll res_y_zero(int N, int M, vector<int> X, vector<int> Y, vector<int> W) {
vector<vector<ll>> dp(2, vector<ll>(N + 5)); // posso prendere a sx o no, posizione
vector<ll> grid(N + 5);
for (int i = 0; i < M; i ++) grid[X[i]] = W[i];
for (int i = N - 1; i >= 0; i --) {
dp[0][i] = dp[1][i + 1];
dp[0][i] = max(dp[0][i], dp[0][i + 1]);
dp[0][i] = max(dp[0][i], dp[0][i + 2] + grid[i + 1]);
dp[0][i] = max(dp[0][i], dp[1][i + 3] + grid[i + 1]);
dp[0][i] = max(dp[0][i], dp[0][i + 3] + grid[i + 1]);
if (i != 0) {
dp[1][i] = dp[1][i + 1];
dp[1][i] = max(dp[1][i], dp[0][i + 1] + grid[i - 1]);
dp[1][i] = max(dp[1][i], dp[0][i + 2] + grid[i - 1] + grid[i + 1]);
dp[1][i] = max(dp[1][i], dp[1][i + 3] + grid[i - 1] + grid[i + 1]);
dp[1][i] = max(dp[1][i], dp[0][i + 3] + grid[i - 1] + grid[i + 1]);
}
}
ll best_res = 0;
for (int i = 0; i <= N; i ++) {
best_res = max(best_res, dp[0][i]);
best_res = max(best_res, dp[1][i]);
}
return best_res;
}
ll cubic(int N, int M, vector<int> X, vector<int> Y, vector<int> W) {
// i, quanto lo alzo, quanto era alzato a destra
// int MAXY = min(N, 9);
int MAXY = N;
ll dp[N + 5][MAXY + 5][MAXY + 5];
for (int i = 0; i < N + 5; i ++) {
for (int j = 0; j < MAXY + 5; j ++) {
for (int k = 0; k < MAXY + 5; k ++) {
dp[i][j][k] = 0;
}
}
}
ll grid[N + 5][MAXY + 5];
for (int i = 0; i < N + 5; i ++) {
for (int j = 0; j < MAXY + 5; j ++) {
grid[i][j] = 0;
}
}
for (int i = 0; i < M; i ++) grid[X[i]][Y[i]] = W[i];
ll ps_grid[N + 5][MAXY + 5]; // 1 based per le Y
for (int i = 0; i < N + 5; i ++) {
ps_grid[i][0] = 0;
for (int j = 0; j < MAXY + 4; j ++) {
ps_grid[i][j + 1] = ps_grid[i][j] + grid[i][j];
}
}
for (int i = N - 1; i >= 0; i --) {
for (int y = 0; y <= MAXY; y ++) {
for (int dx = 0; dx <= MAXY; dx ++) {
// quanto mi alzo
for (int dxdx = 0; dxdx <= MAXY; dxdx ++) {
ll preso = -ps_grid[i][min(dx, y)];
if (y > max(dx, dxdx)) {
preso += ps_grid[i + 1][y] - ps_grid[i + 1][max(dx, dxdx)];
}
if (i > 0) {
preso += ps_grid[i - 1][y];
// cout << " e poi si aggiunge a sx " << ps_grid[i - 1][y] << '\n';
}
// cout << "preso : " << preso << '\n';
// cout << "new value : " << dp[i + 1][dx][dxdx] + preso << '\n';
dp[i][y][dx] = max(dp[i][y][dx], dp[i + 1][dx][dxdx] + preso);
}
}
}
}
ll res = 0;
for (int i = 0; i < N; i ++) {
for (int y = 0; y < MAXY; y ++) {
for (int dx = 0; dx < MAXY; dx ++) {
res = max(res, dp[i][y][dx]);
}
}
}
return res;
}
struct segment {
vector<ll> seg;
segment() {
seg.assign(2 * PW, 0);
}
void update(int x, ll d) {
x += PW;
while (x >= 1) {
seg[x] = max(seg[x], d);
x /= 2;
}
}
ll query(int l, int r) {
l += PW; r += PW;
ll res = 0;
while (l <= r) {
if (l % 2 == 1) {
res = max(res, seg[l]);
l ++;
}
if (r % 2 == 0) {
res = max(res, seg[r]);
r --;
}
l /= 2; r /= 2;
}
return res;
}
};
ll cubic_seg(int N, int M, vector<int> X, vector<int> Y, vector<int> W) {
// i, quanto lo alzo, quanto era alzato a destra
// int MAXY = min(N, 9);
int MAXY = N;
ll dp[N + 5][MAXY + 5][MAXY + 5];
ll seg_no_ps[N + 5][MAXY + 5][MAXY + 5];
ll seg_ps[N + 5][MAXY + 5][MAXY + 5];
for (int i = 0; i < N + 5; i ++) {
for (int j = 0; j < MAXY + 5; j ++) {
for (int k = 0; k < MAXY + 5; k ++) {
dp[i][j][k] = 0;
}
}
}
for (int i = 0; i < N + 5; i ++) {
for (int j = 0; j < MAXY + 5; j ++) {
for (int k = 0; k < MAXY + 5; k ++) {
seg_no_ps[i][j][k] = 0;
seg_ps[i][j][k] = 0;
}
}
}
ll grid[N + 5][MAXY + 5];
for (int i = 0; i < N + 5; i ++) {
for (int j = 0; j < MAXY + 5; j ++) {
grid[i][j] = 0;
}
}
for (int i = 0; i < M; i ++) grid[X[i]][Y[i]] = W[i];
ll ps_grid[N + 5][MAXY + 5]; // 1 based per le Y
for (int i = 0; i < N + 5; i ++) {
ps_grid[i][0] = 0;
for (int j = 0; j < MAXY + 4; j ++) {
ps_grid[i][j + 1] = ps_grid[i][j] + grid[i][j];
}
}
for (int i = N - 1; i >= 0; i --) {
vector<vector<ll>> curr_right_of_dx_right_of_y(MAXY + 1, vector<ll>(MAXY + 1));
for (int dx = 0; dx <= MAXY; dx ++) {
curr_right_of_dx_right_of_y[dx][MAXY] = seg_no_ps[i + 1][dx][MAXY];
for (int y = MAXY - 1; y >= 0; y --) {
curr_right_of_dx_right_of_y[dx][y] = max(
curr_right_of_dx_right_of_y[dx][y + 1], seg_no_ps[i + 1][dx][y]
);
}
}
vector<vector<ll>> curr_left_of_dx(MAXY + 1, vector<ll>(MAXY + 1));
for (int dx = 0; dx <= MAXY; dx ++) {
curr_left_of_dx[dx][0] = seg_no_ps[i + 1][dx][0];
for (int y = 1; y <= MAXY; y ++) {
curr_left_of_dx[dx][y] = max(
curr_left_of_dx[dx][y - 1], seg_no_ps[i + 1][dx][y]
);
}
}
vector<vector<ll>> curr_right_of_dx_left_of_y(MAXY + 1, vector<ll>(MAXY + 1));
for (int dx = 0; dx <= MAXY; dx ++) {
curr_right_of_dx_left_of_y[dx][dx] = seg_ps[i + 1][dx][dx];
for (int y = dx + 1; y <= MAXY; y ++) {
curr_right_of_dx_left_of_y[dx][i] = max(
curr_right_of_dx_left_of_y[dx][y - 1], seg_ps[i + 1][dx][y]
);
}
}
for (int y = 0; y <= MAXY; y ++) {
for (int dx = 0; dx <= MAXY; dx ++) {
ll preso = -ps_grid[i][min(dx, y)];
if (i > 0) preso += ps_grid[i - 1][y];
// dxdx a sinistra di dx;
ll left_of_dx = curr_left_of_dx[dx][dx] + ps_grid[i + 1][max(y, dx)] - ps_grid[i + 1][dx];
// dxdx a destra di dx;
ll right_of_dx_left_of_y = 0;
if (y > dx) {
right_of_dx_left_of_y = curr_right_of_dx_left_of_y[dx][y] + ps_grid[i + 1][y];
}
ll right_of_dx_right_of_y = curr_right_of_dx_right_of_y[dx][max(dx, y)];
dp[i][y][dx] = left_of_dx + preso;
dp[i][y][dx] = max(dp[i][y][dx], right_of_dx_left_of_y + preso);
dp[i][y][dx] = max(dp[i][y][dx], right_of_dx_right_of_y + preso);
seg_no_ps[i][y][dx] = dp[i][y][dx];
seg_ps[i][y][dx] = dp[i][y][dx] - ps_grid[i][dx];
}
}
}
ll res = 0;
for (int i = 0; i < N; i ++) {
for (int y = 0; y <= MAXY; y ++) {
for (int dx = 0; dx <= MAXY; dx ++) {
res = max(res, dp[i][y][dx]);
}
}
}
return res;
}
ll max_weights(int N, int M, vector<int> X, vector<int> Y, vector<int> W) {
bool all_even = 1;
for (auto x : X) if (x % 2) all_even = 0;
if (all_even) return sum_tutto(N, M, X, Y, W);
bool minore_di_due = 1;
for (auto x : X) if (x >= 2) minore_di_due = 0;
if (minore_di_due) return res_minore_di_due(N, M, X, Y, W);
bool y_zero = 1;
for (auto y : Y) if (y > 0) y_zero = 0;
if (y_zero) return res_y_zero(N, M, X, Y, W);
return cubic_seg(N, M, X, Y, W);
}
