#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, …, 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 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