Problem: There are N squares arranged in a row. The squares are numbered 1, 2, ..., N, from left to right.

Snuke is painting each square in red, green or blue. According to his aesthetic sense, the following M conditions must all be satisfied. The i-th condition is:

* There are exactly x_i different colors among squares l_i, l_i + 1, ..., r_i.



In how many ways can the squares be painted to satisfy all the conditions? Find the count modulo 10^9+7.

Constraints

* 1 ≤ N ≤ 300
* 1 ≤ M ≤ 300
* 1 ≤ l_i ≤ r_i ≤ N
* 1 ≤ x_i ≤ 3

Input

Input is given from Standard Input in the following format:


N M
l_1 r_1 x_1
l_2 r_2 x_2
:
l_M r_M x_M


Output

Print the number of ways to paint the squares to satisfy all the conditions, modulo 10^9+7.

Examples

Input

3 1
1 3 3


Output

6


Input

4 2
1 3 1
2 4 2


Output

6


Input

1 3
1 1 1
1 1 2
1 1 3


Output

0


Input

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


Output

108

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

using namespace std;

const int mod = 1e9 + 7;

int N, M;
vector< pair< int, int > > ev[303];
int dp[303][303][303];

bool iroha_check(int iroha, int r, int g, int b) {
  for(auto &p : ev[iroha]) {
    int add = 0;
    add += p.first <= r;
    add += p.first <= g;
    add += p.first <= b;
    if(add != p.second) return false;
  }
  return true;
}

int rec(int r, int g, int b) {
  if(r >= g) swap(r, g);
  if(r >= b) swap(r, b);
  if(g >= b) swap(g, b);
  int &ret = dp[r][g][b];
  if(~ret) return ret;
  if(!iroha_check(b, r, g, b)) return ret = 0;
  if(b == N) return ret = 1;
  ret = 0;
  (ret += rec(b + 1, g, b)) %= mod;
  (ret += rec(r, b + 1, b)) %= mod;
  (ret += rec(r, g, b + 1)) %= mod;
  return ret;
}

int main() {
  cin >> N >> M;
  for(int i = 0; i < M; i++) {
    int l, r, x;
    cin >> l >> r >> x;
    ev[r].emplace_back(l, x);
  }
  memset(dp, -1, sizeof(dp));
  cout << rec(0, 0, 0) << endl;
}