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;
typedef long long ll;
#define rep(i,a) for(int i=0;i<(a);i++)
const ll MOD=1000000007;

int dp[303][303][303];
vector<pair<int,int>> V[333];

int main(){
  int N,M; cin>>N>>M;
  rep(i,M){
    int l,r,x; cin>>l>>r>>x;
    V[r].push_back({l,x});
  }
  ll ans=0;
  dp[0][0][0]=1;
  rep(i,N+1) rep(j,N+1) rep(k,N+1){
    int r=max({i,j,k});
    for(auto p:V[r]){
      int l=p.first, x=p.second, cnt=0;
      if(l<=i&&i<=r) cnt++;
      if(l<=j&&j<=r) cnt++;
      if(l<=k&&k<=r) cnt++;
      if(cnt!=x) dp[i][j][k]=0;
    }
    if(r==N){
      (ans+=dp[i][j][k])%=MOD;
      continue;
    }
    (dp[r+1][j][k]+=dp[i][j][k])%=MOD;
    (dp[i][r+1][k]+=dp[i][j][k])%=MOD;
    (dp[i][j][r+1]+=dp[i][j][k])%=MOD;
  }

  cout<<ans<<endl;
  return 0;
}