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<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int M=310;
const long long mod=1e9+7;
int n,m,id[M][M];
long long f[M][M][M],ans;
struct qury
{
	int l,r,mx;
}q[M];
bool check(int pr,int pg,int pb)
{
//	cout<<pr<<" "<<pg<<" "<<pb<<endl;
	int cnt=0,xx=max(pr,max(pg,pb));
	for(int i=1;i<=id[xx][0];i++)
	{
		cnt=0;
		int ii=id[xx][i];
		if(pr>=q[ii].l)	cnt++;
		if(pg>=q[ii].l) cnt++;
		if(pb>=q[ii].l)	cnt++;
		if(cnt!=q[ii].mx)
		{
			f[pr][pg][pb]=0;
			return 0;
		}
	}
//	cout<<"Yesss"<<endl;
	return 1;
}
int main()
{
	scanf("%d%d",&n,&m);
	for(int i=1;i<=m;i++)	
		scanf("%d%d%d",&q[i].l,&q[i].r,&q[i].mx),id[q[i].r][++id[q[i].r][0]]=i;
	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]==0)
					continue;
				if(check(i,j,k)==0)
					continue;
				int nw=max(i,max(j,k))+1;
				if(nw==n+1)
					(ans+=f[i][j][k])%=mod;
				(f[nw][j][k]+=f[i][j][k])%=mod;
				(f[i][nw][k]+=f[i][j][k])%=mod;
				(f[i][j][nw]+=f[i][j][k])%=mod;
			}
	printf("%lld",ans);
	return 0;
}