#11264Coin Collector

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.

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

6
4