101994: [AtCoder]ABC199 E - Permutation
Memory Limit:256 MB
Time Limit:2 S
Judge Style:Text Compare
Creator:
Submit:0
Solved:0
Description
Score : $500$ points
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 $Y_i$ .
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.
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.
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