github.com/captn3m0/codechef.git

---
category_name: school
problem_code: RD19
problem_name: 'Minimum Deletions'
languages_supported:
    - C
    - CPP14
    - JAVA
    - PYTH
    - 'PYTH 3.5'
    - PYPY
    - CS2
    - 'PAS fpc'
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max_timelimit: '1'
source_sizelimit: '50000'
problem_author: nileshjha19
problem_tester: null
date_added: 2-04-2018
tags:
    - cakewalk
    - gcd
    - may18
    - nileshjha19
editorial_url: 'https://discuss.codechef.com/problems/RD19'
time:
    view_start_date: 1526290200
    submit_start_date: 1526290200
    visible_start_date: 1526290200
    end_date: 1735669800
    current: 1528985554
is_direct_submittable: false
layout: problem
---
All submissions for this problem are available.### Read problems statements in [Mandarin chinese](http://www.codechef.com/download/translated/MAY18/mandarin/RD19.pdf), [Russian](http://www.codechef.com/download/translated/MAY18/russian/RD19.pdf) and [Vietnamese](http://www.codechef.com/download/translated/MAY18/vietnamese/RD19.pdf) as well.

The \*greatest common divisor\* (GCD) of a sequence is the greatest positive integer which divides each element of this sequence. You are given a sequence $A$ of positive integers with size $N$. You are allowed to delete up to $N-1$ elements from this sequence. (I.e., you may delete any number of elements, including zero, as long as the resulting sequence is non-empty.) Please find the minimum number of elements which have to be deleted so that the GCD of the resulting sequence would be equal to $1$, or determine that it is impossible. ### Input - The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows. - The first line of each test case contains a single integer $N$. - The second line contains $N$ space-separated integers $A\_1, A\_2, \\dots, A\_N$. ### Output For each test case, print a single line containing one integer — the minimum number of elements to delete, or $-1$ if it is impossible to make the GCD equal to $1$. ### Constraints - $1 \\le T \\le 100$ - $2 \\le N \\le 1,000$ - $1 \\le A\_i \\le 50,000$ for each valid $i$ ### Subtasks \*\*Subtask #1 (20 points):\*\* $2 \\le N \\le 3$ \*\*Subtask #2 (80 points):\*\* original constraints ### Example Input ``` 2 2 2 3 2 2 4 ``` ### Example Output ``` 0 -1 ``` ### Explanation \*\*Example case 1:\*\* The GCD is already equal to $1$, so the answer is $0$. \*\*Example case 2:\*\* It is impossible to make the GCD equal to $1$, so the answer is $-1$.