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
kotal_kahn: 2017-07-22 17:47:39

why it is showing the wrong answer even though my logic is correct

Shivam Gupta: 2017-03-14 12:29:13

Don't think too much, its a trick question

gajalchouhan: 2017-03-08 09:03:15

please anyone can give me some another example when the print is coming " no".

Anuj Arora: 2016-08-17 22:27:26

Move this to tutorial

siddharth_0196: 2016-06-17 12:04:19

One of the easiest question I have ever solved! :P :D

utkarsh538: 2016-04-13 18:34:15

easy question,just find the logic.

dwij28: 2015-12-27 11:49:28

Its amazing how a matter of time impacts your performance in coding. 3 months ago, I got 5-6 WA's on this, and today it took me 5 minutes to solve this. I am laughing at myself from 3 months ago.. :D

rahul_verma: 2015-10-31 05:19:32

don't care of test case take your own test case

Sarthak Taneja: 2015-08-25 09:55:05

My 250th ... :D

MishThi: 2015-08-08 10:51:12

Easy ques. But, beware of the white spaces in some of the test cases.. :P


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