Problem E
Coin Collector
Input: Standard Input

Output: Standard Output

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 C₁, C₂, ... , C_n the value of each coin type. C₁<C₂<C₃< … <C_n<1000000000. C₁ equals to 1.

Output:

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

Sample Input	Sample Output
2 6 1 2 4 8 16 32 6 1 3 6 8 15 20	6 4

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Problemsetter: Abdullah Al Mahmud

Special Thanks To: Mohammad Mahmudur Rahman