Problem 1331. -- Traveling

1331: Traveling

Time Limit: 1 Sec  Memory Limit: 32 MB   64bit IO Format: %lld
Submitted: 8  Accepted: 6
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SH likes traveling around the world. When he arrives at a city, he will ask the staff about the number of cities that connected with this city directly. After traveling around a mainland, SH will collate data and judge whether the data is correct.

 A group of data is correct when it can constitute an undirected graph.


There are multiple test cases. The first line of each test case is a positive integer N (1<=N<=10000) standing for the number of cities in a mainland. The second line has N positive integers a1, a2, ...,an. ai stands for the number of cities that connected directly with the ith city. Input will be ended by the END OF FILE.


If a group of data is correct, output "YES" in one line, otherwise, output "NO".

Sample Input

7 7 4 3 3 3 2 1
5 4 3 3 2 2 2 1 1 1

Sample Output


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