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 PYTHON3):

Solution:
# coding: utf-8
# Your code here!
import sys
read = sys.stdin.read
readline = sys.stdin.readline

n,m = map(int,readline().split())
#lrx = [tuple(map(int,readline().split())) for _ in range(m)]
#lrx.sort(key=lambda x: x[1])
cond = [[] for _ in range(n+1)]
for _ in range(m):
    l,r,x = map(int,readline().split())
    cond[r].append((l,x))

"""
dp[i][j][k] = iまで見て 2 色目は j個前に、3 色目は k個前 に登場
1 <= j < k
"""
N = n+3
dp = [[0]*(N) for _ in range(N)]
dp[1][2] = 1

MOD = 10**9+7

def f(r,j,k,v,ndp):
    if j >= N or k >= N: return
    for l,x in cond[r]:
        if x==1 and l <= r-j: return
        if x==2 and (r-j < l or l <= r-k): return
        if x==3 and r-k < l: return
    ndp[j][k] += v
    ndp[j][k] %= MOD
    return

for i in range(1,n+1):
    ndp = [[0]*(N) for _ in range(N)]
    for q in range(1,N):
        for r in range(q+1,N):
            v = dp[q][r]
            if v:
                f(i,q+1,r+1,v,ndp)
                f(i,1,r+1,v,ndp)
                f(i,1,q+1,v,ndp)
    dp = ndp
    #print(dp)



ans = sum(sum(i) for i in dp)
print(ans%MOD)