Little Anay is afraid of darkness. He has N candles where height of each candle is known. First day he needs to light 1 candle, Second day he needs to light 2, and so on, till it is possible. If a candle is lit, its height gets reduced by 1 each day. He can also extinguish the candle but only at the end of the day. He wants to know the maximum days he can spend with N candles . But, unable to do so, He seeks for your help. You being the elder cousin of Anay, write a program for him to find the maximum days that he can cover using N candles.

INPUT

First line contain T no of test cases

Second line of input contains an integer M. then, next line contains M integers as height of Candles N, separated by spaces.

OUTPUT

Print the maximum number of days he can be away from darkness.

Constraints:

0<=N<=25000

1<=t<=1000000