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 C1, C2, ... , Cn the value of each coin type. C1<C2<C3<  <Cn<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

Author

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