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 <algorithm>
#define repu(i,x,y) for (int i=x; i<=y; ++i)
using namespace std;

typedef long long LL;
const int p=1000000007;
int n,m,f[310][310][310],l[310],r[310],x[310],ans;

int main()
{
    scanf("%d%d",&n,&m);
    repu(i,1,m)
        scanf("%d%d%d",&l[i],&r[i],&x[i]);
    f[1][0][0]=3;
    repu(i,1,n)
    {
        int l1=-1,r1=n+1,l2=-1,r2=n+1;
        repu(j,1,m)
            if (r[j]==i)
            {
                if (x[j]==1)
                    r1=min(r1,l[j]-1);
                if (x[j]==2)
                    l1=max(l1,l[j]),r2=min(r2,l[j]-1);
                if (x[j]==3)
                    l2=max(l2,l[j]);
            }
        repu(j,l1,r1)
            repu(k,l2,min(r2,j))
                if (f[i][j][k])
                {
                    if (i==n)
                        (ans+=f[i][j][k])%=p;
                    (f[i+1][j][k]+=f[i][j][k])%=p;
                    (f[i+1][i][j]+=f[i][j][k])%=p;
                    (f[i+1][i][k]+=f[i][j][k])%=p;
                }
    }
    printf("%d\n",ans);
    return 0;
}