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 rep(i,x,y) for (int i=(x);i<=(y);i++)
#define ll long long
#define inf 1000000001
#define pii pair<int,int>
#define fi first
#define se second
using namespace std;
#define N 305
#define mod 1000000007
int n,m,f[N][N][N],ans;vector<pii> a[N];
void upd(int &x,int y){x+=y;x-=x>=mod?mod:0;}
bool check(int i,int j,int k,int nw){
	for (auto x:a[nw]){
		int tmp=(i>=x.fi)+(j>=x.fi)+(k>=x.fi);
		if (tmp!=x.se) return 0;
	}
	return 1;
}
int main(){
	scanf("%d%d",&n,&m);
	rep (i,1,m){
		int l,r,x;scanf("%d%d%d",&l,&r,&x);
		a[r].push_back(pii(l,x));
	}
	f[0][0][0]=1;
	rep (i,0,n) rep (j,0,n) rep (k,0,n) if (f[i][j][k]){
		int nw=max(i,max(j,k));
		if (!check(i,j,k,nw)){f[i][j][k]=0;continue;}
		if (nw==n) upd(ans,f[i][j][k]);
		nw++;
		upd(f[nw][j][k],f[i][j][k]);
		upd(f[i][nw][k],f[i][j][k]);
		upd(f[i][j][nw],f[i][j][k]);
	}
	cout<<ans<<'\n';
	return 0;
}