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 Ruby (2.3.3) (judge verdict: Wrong Answer)

N, M = gets.split.map(&:to_i)
MOD = 10**9+7
start = Array.new(N+1){Array.new(3)}
M.times do
    l, r, x = gets.split.map(&:to_i)
    start[r][x-1] = l if !start[r][x-1] || start[r][x-1] > l
end

ans = 0
dp = Array.new(N+1){Array.new(N+1){Array.new(N+1, 0)}}
dp[1][0][0] = 1
dp[0][1][0] = 1
dp[0][0][1] = 1
(2..N).each do |sum|
    s1, s2, s3 = start[sum]
    (0..sum).each do |r|
        (0..(sum-r)).each do |g|
            b = sum-r-g
            if (!s1 || ( g <  s1 &&  b <  s1  )) &&
               (!s2 || ((g <  s2) ^ (b <  s2) )) &&
               (!s3 || ( g >= s3 &&  b >= s3  ))
                dp[r][g][b] += dp[r-1][g][b] if r > 0
            end
            if (!s1 || ( r <  s1 &&  b <  s1  )) &&
               (!s2 || ((r <  s2) ^ (b <  s2) )) &&
               (!s3 || ( r >= s3 &&  b >= s3  ))
                dp[r][g][b] += dp[r][g-1][b] if g > 0
            end
            if (!s1 || ( g <  s1 &&  r <  s1  )) &&
               (!s2 || ((g <  s2) ^ (r <  s2) )) &&
               (!s3 || ( g >= s3 &&  r >= s3  ))
                dp[r][g][b] += dp[r][g][b-1] if b > 0
            end
            dp[r][g][b] %= MOD
            if sum == N
                ans += dp[r][g][b]
                ans %= MOD
            end
        end
    end
end
puts ans