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>
using namespace std;
int f[305][305][305],n,m,ans,l,r,x;const int P=1e9+7;vector<pair<int,int> >v[305];
bool chk(int r,int g,int b)
{
    for(int t=max(r,max(g,b)),i=0;i<v[t].size();i++)
    {
        int l=v[t][i].first,x=v[t][i].second,tot=(r>=l)+(g>=l)+(b>=l);
        if(tot!=x) return 0;
    }
    return 1;
}
int main()
{
    scanf("%d%d",&n,&m);f[0][0][0]=1;
    for(int i=1;i<=m;i++) scanf("%d%d%d",&l,&r,&x),v[r].push_back(make_pair(l,x));
    for(int r=0;r<=n;r++) for(int g=0;g<=n;g++) for(int b=0;b<=n;b++)
    {
        if(!f[r][g][b]) continue;
        if(!chk(r,g,b)){f[r][g][b]=0;continue;}
        int t=max(r,max(g,b))+1;if(t==n+1) ans=(ans+f[r][g][b])%P;
        (f[t][g][b]+=f[r][g][b])%=P;(f[r][t][b]+=f[r][g][b])%=P;(f[r][g][t]+=f[r][g][b])%=P;
    }
    printf("%d\n",ans);
}