A15459 · Bestie · GESP考级

题目描述

You are given an array $a$ consisting of $n$ integers $a_1, a_2, \ldots, a_n$ . Friends asked you to make the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of all numbers in the array equal to $1$ . In one operation, you can do the following: - Select an arbitrary index in the array $1 \leq i \leq n$ ; - Make $a_i = \gcd(a_i, i)$ , where $\gcd(x, y)$ denotes the GCD of integers $x$ and $y$ . The cost of such an operation is $n - i + 1$ . You need to find the minimum total cost of operations we need to perform so that the GCD of the all array numbers becomes equal to $1$ .

Each test consists of multiple test cases. The first line contains an integer $t$ ( $1 \leq t \leq 5\,000$ ) — the number of test cases. The description of test cases follows. The first line of each test case contains a single integer $n$ ( $1 \leq n \leq 20$ ) — the length of the array. The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \leq a_i \leq 10^9$ ) — the elements of the array.

For each test case, output a single integer — the minimum total cost of operations that will need to be performed so that the GCD of all numbers in the array becomes equal to $1$ . We can show that it's always possible to do so.

输入 #1

9
1
1
1
2
2
2 4
3
3 6 9
4
5 10 15 20
5
120 60 80 40 80
6
150 90 180 120 60 30
6
2 4 6 9 12 18
6
30 60 90 120 125 125

输出 #1