CF1732A.Bestie

普及/提高-

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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) 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 $1$ .

输入格式

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.

输出格式

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.

输入输出样例

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

说明/提示

In the first test case, the GCD of the entire array is already equal to $1$ , so there is no need to perform operations.

In the second test case, select $i = 1$ . After this operation, $a_1 = \gcd(2, 1) = 1$ . The cost of this operation is $1$ .

In the third test case, you can select $i = 1$ , after that the array $a$ will be equal to $[1, 4]$ . The GCD of this array is $1$ , and the total cost is $2$ .

In the fourth test case, you can select $i = 2$ , after that the array $a$ will be equal to $[3, 2, 9]$ . The GCD of this array is $1$ , and the total cost is $2$ .

In the sixth test case, you can select $i = 4$ and $i = 5$ , after that the array $a$ will be equal to $[120, 60, 80, 4, 5]$ . The GCD of this array is $1$ , and the total cost is $3$ .

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