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;
ll ans;
ll dp[305][305][305];
vector<pair<int,int>> Q[305];


int main()
{
	int n,m;
	cin>>n>>m;
	for(int i=0;i<m;i++)
	{
		int l,r,x;
		cin>>l>>r>>x;
		Q[r].emplace_back(l,x);
	}
	dp[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(dp[i][j][k]==0)continue;
				int ma=max(i,max(j,k));
				bool ok=1;
				for(auto q : Q[ma])
				{
					int cnt=0;
					if(q.first<=i)cnt++;
					if(q.first<=j)cnt++;
					if(q.first<=k)cnt++;
					if(cnt!=q.second){ok=0;break;}
				}
				if(!ok)continue;
				dp[i][j][k]%=1000000007;
				if(ma==n)ans+=dp[i][j][k];
				dp[ma+1][j][k]+=dp[i][j][k];
				dp[i][ma+1][k]+=dp[i][j][k];
				dp[i][j][ma+1]+=dp[i][j][k];
			}
	ans%=1000000007;
	cout<<ans<<endl;
}