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<cstdio>
#include<cstring>
#include<algorithm>
#include<vector>
#define N 310
#define mod 1000000007
#define pa(a, b) (data){a, b}
using namespace std;
struct data{int x, y;};
int n, m, x, y, z, f[N][N][N], ans;
vector<data>son[N];
inline int check(int x, int y, int i){
	for(int j=0; j<son[i].size(); j++){
		if(son[i][j].y==1&&son[i][j].x<=y)return 0;
		if(son[i][j].y==2&&(son[i][j].x<=x||son[i][j].x>y))return 0;
		if(son[i][j].y==3&&son[i][j].x>x)return 0;
	}
	return 1;
}
int main(){
	scanf("%d%d", &n, &m);
	for(int i=1; i<=n; i++)son[i].clear();
	for(int i=1; i<=m; i++){scanf("%d%d%d", &x, &y, &z); son[y].push_back(pa(x, z));}
	memset(f, 0, sizeof(f)); f[0][0][0]=1;
	for(int i=0; i<=n-1; i++)
		for(int j=0; j<=i; j++)
			for(int k=j; k<=i; k++)if(f[i][j][k]){
				if(check(j, k, i+1))f[i+1][j][k]=(f[i+1][j][k]+f[i][j][k])%mod;
				if(check(k, i, i+1))f[i+1][k][i]=(f[i+1][k][i]+f[i][j][k])%mod;
				if(check(j, i, i+1))f[i+1][j][i]=(f[i+1][j][i]+f[i][j][k])%mod;
			}
	ans=0;
	for(int i=0; i<=n; i++)
		for(int j=i; j<=n; j++)ans=(ans+f[n][i][j])%mod;
	printf("%d", ans);
	return 0;
}