Description

After superman managed to solve the problem whether several sticks can form a triangle, now he thinks of a more advanced problem whether some sticks can form an equilateral triangle (None of them can be bended).

Input

Given an integer n (3<=n<=30), which means the total number of sticks (Number 0 indicates the end of input). And n integers followed by mean the different length of such sticks(1<=len[i]<=100).

Output

If such sticks can form an equilateral triangle (All of them should be used), please print “Yes”, or print the word “No”.

Sample

Input

3 100 100 100 
4 10 10 10 20
0

Output

Yes
No

Hint

It is not guaranteed that given sticks can form a triangle, saying nothing of an equilateral triangle.