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:
// copied
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> ii;
const int N=3e2+5;
const int M=3e2+5;
const ll mod=1e9+7;
ll dp[N][N][N];
int n,m;
vector<ii> v[N];//
bool check(int r,int g,int b)
{
	int k=max(r,max(g,b));
	for(int j=0;j<v[k].size();j++)
	{
		int l=v[k][j].first,x=v[k][j].second;
		int cnt=0;
		if(r>=l)	cnt++;
		if(g>=l)	cnt++;
		if(b>=l) 	cnt++;
		if(cnt!=x)
			return false;
	}
	return true;
}
int main()
{
	while(cin>>n>>m)
	{
		for(int i=1;i<=n;i++)
			v[i].clear();
		int l,r,x;
		for(int i=1;i<=m;i++)
		{
			cin>>l>>r>>x;
			v[r].push_back(ii(l,x));
		}
		memset(dp,0,sizeof(dp));
		dp[0][0][0]=1;
		ll ans=0;
		for(int r=0;r<=n;r++)
		{
			for(int g=0;g<=n;g++)
			{
				for(int b=0;b<=n;b++)
				{
					if(dp[r][g][b]==0)//非法
						continue;
					if(!check(r,g,b))
					{
						dp[r][g][b]=0;
						continue;
					}
					int k=max(r,max(g,b))+1;
					if(k==n+1)
						ans=(ans+dp[r][g][b])%mod;
					dp[k][g][b]+=dp[r][g][b]%mod;
					dp[r][k][b]+=dp[r][g][b]%mod;
					dp[r][g][k]+=dp[r][g][b]%mod;
				}
			}
		}
		cout<<ans<<endl;
	}
	return 0;
}