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>
const int N=305,mo=1e9+7;
using namespace std;
inline int gi(){
  char ch=getchar();int x=0,q=0;
  while(ch<'0' || ch>'9') ch=='-'?q=1:0,ch=getchar();
  while(ch>='0' && ch<='9') x=x*10+ch-'0',ch=getchar();
  return q?(-x):x;
}
int head[N],nn[N],l[N],x[N],cnt,f[N][N][N];
inline void dp(int &x,int y){
  x+=y; if (x>=mo) x-=mo;
  return;
}
inline int Max(int a,int b){
  return a>b?a:b;
}
int main(){
  int n=gi(),m=gi(),a,b,c,ans=0;
  for (int i=1; i<=m; ++i){
    a=gi(),b=gi(),c=gi();
    nn[++cnt]=head[b],head[b]=cnt;
    x[cnt]=c,l[cnt]=a;
  }
  f[0][0][0]=1;
  for (int i=0; i<=n; ++i)
    for (int j=0; j<=n; ++j)
      for (int k=0; k<=n; ++k)
	if (f[i][j][k]){
	  c=Max(Max(i,j),k),b=1;
	  for (a=head[c]; a; a=nn[a])
	    if ((i>=l[a])+(j>=l[a])+(k>=l[a])!=x[a])
	      { b=0; break; }
	  if (!b) continue;
	  if (c==n){
	    dp(ans,f[i][j][k]);
	    continue;
	  }
	  dp(f[c+1][j][k],f[i][j][k]);
	  dp(f[i][c+1][k],f[i][j][k]);
	  dp(f[i][j][c+1],f[i][j][k]);
	}
  cout<<ans;
  return 0;
}