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 mod 1000000007
using namespace std;
const int N=305;
int n,m,mn[N][4],mx[N][4],f[N][N][N],ans;
int check(int a, int b, int c)
{
    if(mn[a][1]<=mx[a][1]) if(mn[a][1]<b+1) return 0;
    if(mn[a][2]<=mx[a][2]) if(mn[a][2]<c+1||b<mx[a][2]) return 0;
    if(mn[a][3]<=mx[a][3]) if(c<mx[a][3]) return 0;
    return 1;
}
int main()
{
    scanf("%d%d",&n,&m);
    for(int i=1;i<=n;i++) for(int j=1;j<=3;j++) mn[i][j]=n+1;
    for(int i=1;i<=m;i++)
    {
        int l,r,x; scanf("%d%d%d",&l,&r,&x);
        mn[r][x]=min(mn[r][x],l);
        mx[r][x]=max(mx[r][x],l);
    }
    f[0][0][0]=1;
    for(int i=0;i<n;i++) for(int j=0;j<=i;j++) for(int k=0;k<=j;k++)
    {
        if(check(i+1,j,k)) (f[i+1][j][k]+=f[i][j][k])%=mod;
        if(check(i+1,i,k)) (f[i+1][i][k]+=f[i][j][k])%=mod;
        if(check(i+1,i,j)) (f[i+1][i][j]+=f[i][j][k])%=mod;
    }
    for (int j=0;j<=n;j++)
        for (int k=0;k<=j;k++)
            (ans+=f[n][j][k])%=mod;
    cout << ans;
}