Problem:
Score : 800 points

Problem Statement

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.

Sample Input 1

3 1
1 3 3

Sample Output 1

6

The six ways are:

RGB

RBG

GRB

GBR

BRG

BGR

where R, G and B correspond to red, green and blue squares, respectively.

Sample Input 2

4 2
1 3 1
2 4 2

Sample Output 2

6

The six ways are:

RRRG

RRRB

GGGR

GGGB

BBBR

BBBG

Sample Input 3

1 3
1 1 1
1 1 2
1 1 3

Sample Output 3

0

There are zero ways.

Sample Input 4

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

Sample Output 4

108

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

from collections import defaultdict
import numpy as np

MOD = 1000000007
iist = lambda: map(int,input().split())

N,M = iist()
Q = defaultdict(list)
for i in range(M):
  l,r,x = iist()
  Q[r].append((l,x-1))

if any(x != 0 for l,x in Q[1]):
  print(0)
  exit(0)

dp = np.zeros((N,N), dtype='i8')
dp[0,0] = 3
memo = np.zeros(N, dtype='i8')
memo[0] = 6
s = 3

for pk in range(1,N):
  k = pk+1
  dp[:pk,pk] = memo[:pk]
  memo[:pk] *= 2
  memo[:pk] %= MOD

  memo[pk] = 2*s%MOD
  s = 3*s%MOD
  subQ = Q[k]

  for i,j in zip(*np.nonzero(dp[:pk,:k])):
    for l,x in subQ:
      if x != int(l<=i)+int(l<=j):
        c = dp[i,j]
        memo[i] -= c
        memo[j] -= c
        s -= c
        dp[i,j] = 0
        break
  s %= MOD

print(s)