Coin exchange

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 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 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

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