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 maxn=3e2+10;
const int mod=1e9+7;
int dp[maxn][maxn][maxn];
vector<int>p[maxn],lim[maxn];
int n,m;
bool check(int a,int b,int c,int x)
{
	for(int i=0;i<p[x].size();i++)
	{
		int cnt=0;
		if(a>=p[x][i])cnt++;
		if(b>=p[x][i])cnt++;
		if(c>=p[x][i])cnt++;
		if(cnt!=lim[x][i])return false;
	}
	return true;
}
inline int md(int x){return x>=mod?x-mod:x;}
int main()
{
	scanf("%d%d",&n,&m);
	for(int i=1;i<=m;i++)
	{
		int l,r,x;
		scanf("%d%d%d",&l,&r,&x);
		p[r].push_back(l);
		lim[r].push_back(x);
	}
	dp[0][0][0]=1;
	for(int i=0;i<=n;i++)
	{
		for(int j=0;j<=i;j++)
		for(int k=0;k<=j;k++)
		{
			if(!check(i,j,k,i)){dp[i][j][k]=0;continue;}
			dp[i+1][j][k]=md(dp[i+1][j][k]+dp[i][j][k]);
			dp[i+1][i][k]=md(dp[i+1][i][k]+dp[i][j][k]);
			dp[i+1][i][j]=md(dp[i+1][i][j]+dp[i][j][k]);
		}
	}
	int ret=0;
	for(int i=0;i<=n;i++)
	for(int j=0;j<=i;j++)ret=md(ret+dp[n][i][j]);
	printf("%d\n",ret);
}