F. Familiar Operations
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given two positive integers $a$ and $b$. There are two possible operations:

1. multiply one of the numbers by some prime $p$;
2. divide one of the numbers on its prime factor $p$.

What is the minimum number of operations required to obtain two integers having the same number of divisors? You are given several such pairs, you need to find the answer for each of them.

Input

The first line contains a single integer $t$ ($1 \le t \le 10^5$) — the number of pairs of integers for which you are to find the answer.

Each of the next $t$ lines contain two integers $a_i$ and $b_i$ ($1 \le a_i, b_i \le 10^6$).

Output

Output $t$ lines — the $i$-th of them should contain the answer for the pair $a_i$, $b_i$.

Example
Input
89 10100 17220 7017 194 1832 20100 32224 385
Output
13101011
Note

These are the numbers with equal number of divisors, which are optimal to obtain in the sample test case:

• $(27, 10)$, 4 divisors
• $(100, 1156)$, 9 divisors
• $(220, 140)$, 12 divisors
• $(17, 19)$, 2 divisors
• $(12, 18)$, 6 divisors
• $(50, 32)$, 6 divisors
• $(224, 1925)$, 12 divisors

Note that there can be several optimal pairs of numbers.