Bobo has a decimal integer $\overline{a_1 a_2 \dots a_n}$, possibly with leading zeros. He knows that for $m$ ranges $[l_1, r_1], [l_2, r_2], \dots, [l_m, r_m]$, it holds that $a_{l_i} \times a_{l_i + 1} \times \dots \times a_{r_i} \bmod 9 = 0$. Find the number of valid integers $\overline{a_1 a_2 \dots a_n}$, modulo $(10^9+7)$.
Input
The input consists of several test cases and is terminated by end-of-file.
The first line of each test case contains two integers $n$ and $m$.
The $i$th of the following $m$ lines contains two integers $l_i$ and $r_i$.
- $1 \leq n, m \leq 50$
- $1 \leq l_i \leq r_i \leq n$
- There are at most $100$ test cases.
Output
For each test case, print an integer which denotes the result.
Sample Input
2 1 1 2 4 2 1 3 2 4 50 1 1 50
Sample Output
40 4528 100268660