Problem Statement

Print the number of sequences a that are permutations of $(1, 2, 3, \dots, N)$ and satisfy the following condition:

• for every integer i such that $1 \le i \le M, at most Z_i numbers among a_1, a_2, a_3, \dots, a_{X_i}$ are less than or equal to Y_i .

Input

Input is given from Standard Input in the following format:
N M
X_1 Y_1 Z_1
X_2 Y_2 Z_2
X_3 Y_3 Z_3
$\hspace{23pt} \vdots$
X_M Y_M Z_M

Output

Print the answer.

Constraints

• $2 \le N \le 18$
• $0 \le M \le 100$
• $1 \le X_i \lt N$
• $1 \le Y_i \lt N$
• $0 \le Z_i \lt N$
• All values in input are integers.

Sample Input 1

3 1
2 2 1

Sample Output 1

4

The four sequences a satisfying the condition are:

• (1, 3, 2)
• (2, 3, 1)
• (3, 1, 2)
• (3, 2, 1)

(1, 2, 3) and (2, 1, 3) violate the condition, since each of them has two numbers less than or equal to 2 among a_1, a_2.

Sample Input 2

5 2
3 3 2
4 4 3

Sample Output 2

90

Sample Input 3

18 0

Sample Output 3

6402373705728000

见题面 Input 部分

见题面 Output 部分