Too Simple

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 65536/65536 K (Java/Others)

Description

Rhason Cheung had a simple problem, and asked Teacher Mai for help. But Teacher Mai thought this problem was too simple, sometimes naive. So she ask you for help.

Teacher Mai has $m$ functions $f_1,f_2,\cdots,f_m:\{1,2,\cdots,n\}\to\{1,2,\cdots,n\}$(that means for all $x \in \{1,2,\cdots,n\},f(x)\in \{1,2,\cdots,n\}$). But Rhason only knows some of these functions, and others are unknown.

She wants to know how many different function series $f_1,f_2,\cdots,f_m$ there are that for every $i(1\leq i\leq n)$,$f_1(f_2(\cdots f_m(i)))=i$. Two function series $f_1,f_2,\cdots,f_m$ and $g_1,g_2,\cdots,g_m$ are considered different if and only if there exist $i(1\leq i\leq m),j(1\leq j\leq n)$,$f_i(j)\neq g_i(j)$.

Input

For each test case, the first lines contains two numbers $n,m(1\leq n,m\leq 100)$.

The following are $m$ lines. In $i$-th line, there is one number $-1$ or $n$ space-separated numbers.

If there is only one number $-1$, the function $f_i$ is unknown. Otherwise the $j$-th number in the $i$-th line means $f_i(j)$.

Output

For each test case print the answer modulo $10^9+7$.

Sample Input

3 3 1 2 3 -1 3 2 1

Sample Output

1
Hint
The order in the function series is determined. What she can do is to assign the values to the unknown functions.

Hint

wange2014

Source

2015 Multi-University Training Contest 9

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