SPCU - Gopu and Validity of Arrangement


N persons are standing in a line. Height of each person is between 1 and N and height of each person is distinct. 

You are  given an array A where A[i] denotes how many persons are there before the i_th person having heights greater than the height of the ith person. For a person i, all the persons from 1 to i - 1 are considered to be before him. eg, For person 2, person 1 is considered before him.

You have to find out whether this array can be valid for some arrangement of persons. If you can uniquely do so then output "YES" Otherwise output "NO".

Input

First line contains T : number of test cases. (1 <= T <= 20).

For each test First line contains an integer n. (1 <= N <= 10^5)

Next line contains n space seperated integers denoting A[i]. (0 <= A[i] <= N)

Output

For each test case, output "YES" or "NO" according to answer.

Example

Input:
2
2
0 1
2
1 1 
Output:
YES
NO

Explanation

  For the first test case, [2, 1] is a valid case, First person has height 2, second person has height 1. 

  For the second test case, no valid test case exists.


hide comments
hrishabh: 2015-07-17 00:39:05

Easy one...!!
Ac in first go :)
Aftr a long time :D

mrx: 2015-06-30 21:19:38

Lol, confidence booster :P

Dhruv k14: 2015-04-02 20:22:20

AC in 1st go after a reaaaallly long time,seriously needed that confidence :)

Sahil Dua: 2015-01-04 00:23:01

Very easy one.
But how can I improve timing, any clue? I got AC in 0.39s

EDIT: Fast I/O with cin.tie(NULL) and passed in 0.01 ;)

Last edit: 2015-01-04 01:39:32
divij: 2014-10-25 20:41:15

cin/cout = WA, scanf = AC .... Same logic

mkrjn99: 2014-09-29 08:19:46

Last edit: 2014-09-29 20:13:57
FoolForCS: 2014-09-28 13:38:26

I think the input is not filtered. Be very careful while using fast io.
scanf = AC.

Last edit: 2014-09-28 13:39:15
Gaara: 2014-02-04 19:04:31

easy one ...:)

Vipul Pandey: 2014-01-23 21:52:43

easy once you get it.

Abhinav Gupta: 2014-01-23 08:28:01

what would be the answer for 0 0


Added by:praveen123
Date:2014-01-08
Time limit:2s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:IITK ACA CSE online judge