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;
const int mod=1e9+7;
vector<int>a[310],b[310];
int f[310][310][310];
inline int read()
{
	int x=0,f=1;char ch=getchar();
	for(;ch<'0'||ch>'9';ch=getchar())if(ch=='-')f=-1;
	for(;ch>='0'&&ch<='9';x=(x<<1)+(x<<3)+ch-'0',ch=getchar());
	return x*f;
}
bool check(int r,int g,int bl)
{
	int i=max(max(r,g),bl),siz=a[i].size();
	for(int j=0;j<siz;j++)
	{
		int l=a[i][j],x=b[i][j];
		if(x!=((r>=l)+(g>=l)+(bl>=l)))return 0;
	}
	return 1;
}
int main()
{
	int n=read(),m=read(),l,r,x,ans=0;
	for(int i=1;i<=m;i++)
	{
		l=read(),r=read(),x=read();
		a[r].push_back(l),b[r].push_back(x);
	}
	f[0][0][0]=1;
	for(int r=0;r<=n;r++)
		for(int g=0;g<=n;g++)if(!g||g!=r)
			for(int b=0;b<=n;b++)if(!b||(b!=g&&b!=r))
			{
				if(!check(r,g,b))
				{
					f[r][g][b]=0;
					continue;
				}
				int i=max(max(r,g),b);
				if(i==n)
					ans=(ans+f[r][g][b])%mod;
				else
				{
					f[i+1][g][b]=(f[i+1][g][b]+f[r][g][b])%mod;
					f[r][i+1][b]=(f[r][i+1][b]+f[r][g][b])%mod;
					f[r][g][i+1]=(f[r][g][i+1]+f[r][g][b])%mod;
				}
			}
	printf("%d\n",ans);
	return 0;
}