#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cstring>

#include <iostream>
#include <complex>
#include <string>
#include <algorithm>
#include <numeric>
#include <vector>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <bitset>

#include <functional>
#include <cassert>

typedef long long ll;
using namespace std;

#ifndef LOCAL
#define debug(x) ;
#else
#define debug(x) cerr << __LINE__ << " : " << #x << " = " << (x) << endl;

template <typename T1, typename T2>
ostream &operator<<(ostream &out, const pair<T1, T2> &p) {
  out << "{" << p.first << ", " << p.second << "}";
  return out;
}

template <typename T>
ostream &operator<<(ostream &out, const vector<T> &v) {
  out << '{';
  for (const T &item : v) out << item << ", ";
  out << "\b\b}";
  return out;
}
#endif

#define mod 1000000007 //1e9+7(prime number)
#define INF 1000000000 //1e9
#define LLINF 2000000000000000000LL //2e18
#define SIZE 200010

/* Li Chao Tree */

template<typename T>
struct LiChaoTree {
  using Line = pair<T, T>; // first * x + second

  int segn2;
  vector<Line> data;
  vector<T> X;

  template<typename S>
  void init(vector<S> pos) {
    int N = pos.size();
    for (segn2 = 1; segn2 < N; segn2 *= 2);
    data.assign(segn2 * 2, {0, -LLINF});
    X.assign(segn2, -LLINF);
    for (int i=0; i<(int)pos.size(); i++)
      X[i] = pos[i];
  }

  inline T f(Line line, T x) {
    return line.first * x + line.second;
  }

  void addLine(int a, int b, Line line, int l = 0, int r = -1, int k = 0) {
    if (r == -1) r = segn2;
    int m = (l + r) / 2;

    if (r <= a || b <= l) return;
    if (l < a || b < r) {
      addLine(a, b, line, l, m, k*2+1);
      addLine(a, b, line, m, r, k*2+2);
      return;
    }
    if (data[k].second == -LLINF) { //isNull
      data[k] = line;
      return;
    }

    bool fl = f(line, X[l])   > f(data[k], X[l]);
    bool fm = f(line, X[m])   > f(data[k], X[m]);
    bool fr = f(line, X[r-1]) > f(data[k], X[r-1]);

    if (fl == fr) {
      if (fl) data[k] = line;
      return;
    }
    if (fm) swap(data[k], line);

    if (fl ^ fm) addLine(a, b, line, l, m, 2*k+1);
    else addLine(a, b, line, m, r, 2*k+2);
  }

  void addLine(Line line) { addLine(0, segn2, line); }

  T query(int k) {
    T x = X[k], res = -LLINF;
    k += segn2-1;

    while(1){
      if (data[k].second != -LLINF) //isNotNull
        res = max(res, f(data[k], x));
      if (!k) break;
      k = (k - 1) / 2;
    }

    return res;
  }
};

pair<pair<int,int>,int> query[SIZE];

int main(){
  int N, M;
  ll X, Y;
  vector<int> pos;
  map<int,int> dic;

  scanf("%d%d%lld%lld", &N, &M, &X, &Y);

  for (int i=0; i<M; i++) {
    int c, l, r;
    scanf("%d%d%d", &c, &l, &r);
    l--; c--;
    pos.push_back(l);
    pos.push_back(r);
    query[i] = {{r, l}, c};
  }

  sort(query, query+M);

  sort(pos.begin(), pos.end());
  pos.erase(unique(pos.begin(), pos.end()), pos.end());
  for (int i=0; i<pos.size(); i++)
    dic[pos[i]] = i;

  LiChaoTree<ll> lct[3][2]; //{color, diff}

  for (int i=0; i<6; i++)
    lct[i/2][i%2].init(pos);

  for (int i=0; i<M; i++) {
    // [l, r)
    int l = query[i].first.second;
    int r = query[i].first.first;
    int c = query[i].second;


    ll v = 0;

    for (int j=0; j<3; j++) {
      v = max(v, lct[j][c != j].query(dic[l]));
    }

    //同じ
    lct[c][0].addLine(dic[l], dic[r], {X, v - l*X});
    lct[c][0].addLine(dic[r], dic.size(), {0, v + (r - l) * X});

    //異なる
    lct[c][1].addLine(dic[l], dic[r], {X + (Y + X), v - (X * l + (Y + X) * r)});
    lct[c][1].addLine(dic[r], dic.size(), {0, v + (r - l) * X});
  }

  ll ans = 0;

  for (int i=0; i<6; i++) {
    ans = max(ans, lct[i/2][i%2].query((int)dic.size()-1));
  }

  cout << ans << endl;

  return 0;
}


### Prompt

Your task is to create a Cpp solution to the following problem:

Wall Painting

Here stands a wall made of a number of vertical panels. The panels are not painted yet.

You have a number of robots each of which can paint panels in a single color, either red, green, or blue. Each of the robots, when activated, paints panels between a certain position and another certain position in a certain color. The panels painted and the color to paint them are fixed for each of the robots, but which of them are to be activated and the order of their activation can be arbitrarily decided.

You’d like to have the wall painted to have a high aesthetic value. Here, the aesthetic value of the wall is defined simply as the sum of aesthetic values of the panels of the wall, and the aesthetic value of a panel is defined to be:

* 0, if the panel is left unpainted.
* The bonus value specified, if it is painted only in a single color, no matter how many times it is painted.
* The penalty value specified, if it is once painted in a color and then overpainted in one or more different colors.



Input

The input consists of a single test case of the following format.


$n$ $m$ $x$ $y$
$c_1$ $l_1$ $r_1$
.
.
.
$c_m$ $l_m$ $r_m$


Here, $n$ is the number of the panels ($1 \leq n \leq 10^9$) and $m$ is the number of robots ($1 \leq m \leq 2 \times 10^5$). $x$ and $y$ are integers between $1$ and $10^5$, inclusive. $x$ is the bonus value and $-y$ is the penalty value. The panels of the wall are consecutively numbered $1$ through $n$. The $i$-th robot, when activated, paints all the panels of numbers $l_i$ through $r_i$ ($1 \leq l_i \leq r_i \leq n$) in color with color number $c_i$ ($c_i \in \\{1, 2, 3\\}$). Color numbers 1, 2, and 3 correspond to red, green, and blue, respectively.

Output

Output a single integer in a line which is the maximum achievable aesthetic value of the wall.

Sample Input 1


8 5 10 5
1 1 7
3 1 2
1 5 6
3 1 4
3 6 8


Sample Output 1


70


Sample Input 2


26 3 9 7
1 11 13
3 1 11
3 18 26


Sample Output 2


182


Sample Input 3


21 10 10 5
1 10 21
3 4 16
1 1 7
3 11 21
3 1 16
3 3 3
2 1 17
3 5 18
1 7 11
2 3 14


Sample Output 3


210


Sample Input 4


21 15 8 7
2 12 21
2 1 2
3 6 13
2 13 17
1 11 19
3 3 5
1 12 13
3 2 2
1 12 15
1 5 17
1 2 3
1 1 9
1 8 12
3 8 9
3 2 9


Sample Output 4


153






Example

Input

8 5 10 5
1 1 7
3 1 2
1 5 6
3 1 4
3 6 8


Output

70

### Response

```cpp
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cstring>

#include <iostream>
#include <complex>
#include <string>
#include <algorithm>
#include <numeric>
#include <vector>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <bitset>

#include <functional>
#include <cassert>

typedef long long ll;
using namespace std;

#ifndef LOCAL
#define debug(x) ;
#else
#define debug(x) cerr << __LINE__ << " : " << #x << " = " << (x) << endl;

template <typename T1, typename T2>
ostream &operator<<(ostream &out, const pair<T1, T2> &p) {
  out << "{" << p.first << ", " << p.second << "}";
  return out;
}

template <typename T>
ostream &operator<<(ostream &out, const vector<T> &v) {
  out << '{';
  for (const T &item : v) out << item << ", ";
  out << "\b\b}";
  return out;
}
#endif

#define mod 1000000007 //1e9+7(prime number)
#define INF 1000000000 //1e9
#define LLINF 2000000000000000000LL //2e18
#define SIZE 200010

/* Li Chao Tree */

template<typename T>
struct LiChaoTree {
  using Line = pair<T, T>; // first * x + second

  int segn2;
  vector<Line> data;
  vector<T> X;

  template<typename S>
  void init(vector<S> pos) {
    int N = pos.size();
    for (segn2 = 1; segn2 < N; segn2 *= 2);
    data.assign(segn2 * 2, {0, -LLINF});
    X.assign(segn2, -LLINF);
    for (int i=0; i<(int)pos.size(); i++)
      X[i] = pos[i];
  }

  inline T f(Line line, T x) {
    return line.first * x + line.second;
  }

  void addLine(int a, int b, Line line, int l = 0, int r = -1, int k = 0) {
    if (r == -1) r = segn2;
    int m = (l + r) / 2;

    if (r <= a || b <= l) return;
    if (l < a || b < r) {
      addLine(a, b, line, l, m, k*2+1);
      addLine(a, b, line, m, r, k*2+2);
      return;
    }
    if (data[k].second == -LLINF) { //isNull
      data[k] = line;
      return;
    }

    bool fl = f(line, X[l])   > f(data[k], X[l]);
    bool fm = f(line, X[m])   > f(data[k], X[m]);
    bool fr = f(line, X[r-1]) > f(data[k], X[r-1]);

    if (fl == fr) {
      if (fl) data[k] = line;
      return;
    }
    if (fm) swap(data[k], line);

    if (fl ^ fm) addLine(a, b, line, l, m, 2*k+1);
    else addLine(a, b, line, m, r, 2*k+2);
  }

  void addLine(Line line) { addLine(0, segn2, line); }

  T query(int k) {
    T x = X[k], res = -LLINF;
    k += segn2-1;

    while(1){
      if (data[k].second != -LLINF) //isNotNull
        res = max(res, f(data[k], x));
      if (!k) break;
      k = (k - 1) / 2;
    }

    return res;
  }
};

pair<pair<int,int>,int> query[SIZE];

int main(){
  int N, M;
  ll X, Y;
  vector<int> pos;
  map<int,int> dic;

  scanf("%d%d%lld%lld", &N, &M, &X, &Y);

  for (int i=0; i<M; i++) {
    int c, l, r;
    scanf("%d%d%d", &c, &l, &r);
    l--; c--;
    pos.push_back(l);
    pos.push_back(r);
    query[i] = {{r, l}, c};
  }

  sort(query, query+M);

  sort(pos.begin(), pos.end());
  pos.erase(unique(pos.begin(), pos.end()), pos.end());
  for (int i=0; i<pos.size(); i++)
    dic[pos[i]] = i;

  LiChaoTree<ll> lct[3][2]; //{color, diff}

  for (int i=0; i<6; i++)
    lct[i/2][i%2].init(pos);

  for (int i=0; i<M; i++) {
    // [l, r)
    int l = query[i].first.second;
    int r = query[i].first.first;
    int c = query[i].second;


    ll v = 0;

    for (int j=0; j<3; j++) {
      v = max(v, lct[j][c != j].query(dic[l]));
    }

    //同じ
    lct[c][0].addLine(dic[l], dic[r], {X, v - l*X});
    lct[c][0].addLine(dic[r], dic.size(), {0, v + (r - l) * X});

    //異なる
    lct[c][1].addLine(dic[l], dic[r], {X + (Y + X), v - (X * l + (Y + X) * r)});
    lct[c][1].addLine(dic[r], dic.size(), {0, v + (r - l) * X});
  }

  ll ans = 0;

  for (int i=0; i<6; i++) {
    ans = max(ans, lct[i/2][i%2].query((int)dic.size()-1));
  }

  cout << ans << endl;

  return 0;
}


```