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>
#define ll long long
#define pii pair<int,int>
#define mp make_pair
#define fst first
#define snd second
#define pb push_back
using namespace std;
const int N=310;
const ll P=1e9+7;
vector<pii>q[N];
ll dp[N][N][N];
int main(){
	int n,m;
	scanf("%d%d",&n,&m);
	while(m--){
		int x,y,z;
		scanf("%d%d%d",&x,&y,&z);
		q[y].pb(mp(x,z));
	}
	dp[1][0][0]=3;//注意dp[1][0][0]有3种取色方案
	for(int i=1;i<=n;++i){
		for(int j=0;j<q[i].size();++j){
			int x=q[i][j].fst,z=q[i][j].snd;
			for(int k=0;k<i;++k)
				for(int p=0;p<=max(0,k-1);++p){
					if(z==1&&k>=x)dp[i][k][p]=-1;
					if(z==2&&(k<x||p>=x))dp[i][k][p]=-1;
					if(z==3&&p<x)dp[i][k][p]=-1;
			}
		}
		if(i==n)break;
		for(int j=0;j<i;++j)
			for(int k=0;k<=max(0,j-1);++k){
				if(dp[i][j][k]==-1)continue;
				(dp[i+1][j][k]+=dp[i][j][k])%=P;
			(dp[i+1][i][k]+=dp[i][j][k])%=P;
				(dp[i+1][i][j]+=dp[i][j][k])%=P;
		}
	}
	ll ans=0;
	for(int j=0;j<n;++j)
		for(int k=0;k<=max(0,j-1);++k)
			if(dp[n][j][k]!=-1)
				(ans+=dp[n][j][k])%=P;
	printf("%lld\n",ans);
	return 0;
}