github.com/captn3m0/codechef.git

---
category_name: easy
problem_code: AMSGAME2
problem_name: 'Subtraction Game 2'
languages_supported:
    - ADA
    - ASM
    - BASH
    - BF
    - C
    - 'C99 strict'
    - CAML
    - CLOJ
    - CLPS
    - 'CPP 4.3.2'
    - 'CPP 4.9.2'
    - CPP14
    - CS2
    - D
    - ERL
    - FORT
    - FS
    - GO
    - HASK
    - ICK
    - ICON
    - JAVA
    - JS
    - 'LISP clisp'
    - 'LISP sbcl'
    - LUA
    - NEM
    - NICE
    - NODEJS
    - 'PAS fpc'
    - 'PAS gpc'
    - PERL
    - PERL6
    - PHP
    - PIKE
    - PRLG
    - PYTH
    - 'PYTH 3.4'
    - RUBY
    - SCALA
    - 'SCM guile'
    - 'SCM qobi'
    - ST
    - TCL
    - TEXT
    - WSPC
max_timelimit: '1'
source_sizelimit: '50000'
problem_author: 'satej '
problem_tester: gamabunta
date_added: 11-05-2013
tags:
    - cook34
    - dynamic
    - satej
    - simple
editorial_url: 'http://discuss.codechef.com/problems/AMSGAME2'
time:
    view_start_date: 1368988200
    submit_start_date: 1368988200
    visible_start_date: 1368988200
    end_date: 1735669800
    current: 1493558211
layout: problem
---
All submissions for this problem are available.Chef is playing a game on a sequence of **N** positive integers, say **A1, A2, ... AN**. The game is played as follows.

- If all the numbers are equal, the game ends.
- Otherwise 
  - Select two numbers which are unequal
  - Subtract the smaller number from the larger number
  - Replace the larger number with the result from above

Chef has already figured out that the game **always terminates**. He also knows, for a given sequence of integers, the game will always terminate on the **same value**, no matter how the game is played. Chef wants you to simulate the game for him and tell him if the game terminates on **1**.

In fact, there may be many such games. Given a sequence of integers Chef wants to know the number of **sub-sequences** of the given sequence, for which, playing the above game on the subsuquence will terminate on **1**. A **sub-sequence** can be obtained from the original sequence by **deleting 0 or more** integers from the original sequence. See the explanation section for clarity.

### Input

The first line of the input contains an integer **T**, the number of test cases. Then follow the description of **T** test cases. The first line of each test case contains a single integer **N**, the length of the sequence. The second line contains **N** positive integers, each separated by a single space.

### Output

For each test case, **output a single integer** - the number of **sub-sequences** of the original sequence, such that, playing the game on the **sub-sequence** results in ending the game with all the values equal to **1**.

### Constraints

**1 ≤ T ≤ 100**
**1 ≤ N ≤ 60**
**1 ≤ Ai ≤ 104**
**All Ai will be distinct.**

### Sample

<pre>
<b>Input</b>
3
4
2 3 5 7
4
3 4 8 16
3
6 10 15

<b>Output</b>
11
7
1

</pre>### Explanation

**Test Case 1:** The following 11 sub-sequences are counted.

- { 2, 3 }
- { 2, 5 }
- { 2, 7 }
- { 3, 5 }
- { 3, 7 }
- { 5, 7 }
- { 2, 3, 5 }
- { 2, 3, 7 }
- { 2, 5, 7 }
- { 3, 5, 7 }
- { 2, 3, 5, 7 }

**Test Case 2:** The following 7 sub-sequences are counted.

- { 3, 4 }
- { 3, 8 }
- { 3, 16 }
- { 3, 4, 8 }
- { 3, 4, 16 }
- { 3, 8, 16 }
- { 3, 4, 8, 16 }

**Test Case 3:** There are 8 subsequences of { 6, 10, 15 }

- {} => The game cannot be played on this sub-sequence
- { 6 } => The game cannot be played on this sub-sequence
- { 10 } => The game cannot be played on this sub-sequence
- { 15 } => The game cannot be played on this sub-sequence
- { 6, 10 } => The game cannot end at { 1, 1 }
- { 6, 15 } => The game cannot end at { 1, 1 }
- { 10, 15 } => The game cannot end at { 1, 1 }
- { 6, 10, 15 } => The game ends at { 1, 1, 1 }. Hence this is the only sub-sequence that is counted in the result.