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<cstdio>
#include<cstring>
#include<vector>
using namespace std;
#define MN 300
#define MOD 1000000007
int f[2][MN+5][MN+5];
vector< pair<int,int> > v[MN+5];
inline void rw(int&a,int b){if((a+=b)>=MOD)a-=MOD;}
int main()
{
	int n,m,l,r,i,j,k,ans=0;
	scanf("%d%d",&n,&m);
	while(m--)scanf("%d%d%d",&l,&r,&i),v[r].push_back(make_pair(l,i));
	f[0][0][0]=1;
	for(i=0;i<n;++i)
	{
		memset(f[~i&1],0,sizeof(f[~i&1]));
		for(j=0;j<=i;++j)for(k=0;k<=j;++k)if(f[i&1][j][k])
			rw(f[~i&1][j][k],f[i&1][j][k]),
			rw(f[~i&1][i][k],f[i&1][j][k]),
			rw(f[~i&1][i][j],f[i&1][j][k]);
		for(l=0;l<v[i+1].size();++l)for(j=0;j<=i;++j)for(k=0;k<=j;++k)
			if(1+(j>=v[i+1][l].first)+(k>=v[i+1][l].first)!=v[i+1][l].second)f[~i&1][j][k]=0;
		if(i+1==n)for(j=0;j<=i;++j)for(k=0;k<=j;++k)rw(ans,f[~i&1][j][k]);
	}
	printf("%d",ans);
}