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;
#define maxn 305
#define mod 1000000007
int n,m;
int rec[maxn][maxn][maxn];
int mem[maxn][maxn][maxn];
vector<pair<int,int> > q[maxn];
bool check(int a,int b,int c)
{
    int i,x = max(a,max(b,c)),now;
    if(rec[a][b][c]==-1) {
        rec[a][b][c] = 1;
        for(i=0;i<q[x].size();i++)
        {
            now = (q[x][i].first<=a) + (q[x][i].first<=b) + (q[x][i].first<=c);
            if(q[x][i].second!=now) rec[a][b][c] = 0;
        }
    }
    return rec[a][b][c];
}
int f(int a,int b,int c)
{
    int x = max(a,max(b,c)) + 1;
    if(x==n+1) return check(a,b,c);
    if(mem[a][b][c]==-1) {
        if(!check(a,b,c)) mem[a][b][c] = 0;
        else mem[a][b][c] = (f(x,b,c) + (f(a,x,c) + f(a,b,x))%mod)%mod;
    }
    return mem[a][b][c];
}
int main()
{
    int i,x,y,val;
    scanf("%d%d",&n,&m);
    for(i=1;i<=m;i++)
    {
        scanf("%d%d%d",&x,&y,&val);
        q[y].push_back({x,val});
    }
    memset(rec,-1,sizeof(rec));
    memset(mem,-1,sizeof(mem));
    printf("%d",f(0,0,0));
}