# Coin exchange

Time limit: 5 seconds
## Problem

Our dear Sultan is visiting a
country where there are **n** different types of coin. He wants to collect
as many different types of coin as you can. Now if he wants to withdraw **X**
amount of money from a Bank, the Bank will give him this money using following
algorithm.

withdraw(X){
if( X == 0) return;
Let Y be the highest valued coin that does not exceed X.
Give the customer Y valued coin.
withdraw(X-Y);
}

Now Sultan can withdraw any amount
of money from the Bank. He should maximize the number of different coins that
he can collect in a single withdrawal.

## Input

First line of the input contains
**T** the number of test cases. Each of the test cases starts with **n (1≤n≤1000)**, the number of different types of coin.
Next line contains n integers **C**_{1}, C_{2}, ... , C_{n}
the value of each coin type. **C**_{1}<C_{2}<C_{3}< … <C_{n}<1000000000.
**C**_{1} equals to 1.

## Output

** **

For each test case output one
line denoting the maximum number of types of coins that Sultan can collect in a single
withdrawal. He can withdraw infinite amount of money from the Bank.

## Sample input

2
6
1 2 4 8 16 32
6
1 3 6 8 15 20

## Sample output

6
4

## Author

Copied from UVA