Codeforces Round #371 (Div. 2) B. Filya and Homework

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题目点我点我点我

Today, hedgehog Filya went to school for the very first time! Teacher gave him a homework which Filya was unable to complete without your help.

Filya is given an array of non-negative integers a1, a2, ..., an. First, he pick an integer x and then he adds x to some elements of the array (no more than once), subtract x from some other elements (also, no more than once) and do no change other elements. He wants all elements of the array to be equal.

Now he wonders if it's possible to pick such integer x and change some elements of the array using this x in order to make all elements equal.

Input

The first line of the input contains an integer n (1 ≤ n ≤ 100 000) — the number of integers in the Filya's array. The second line containsn integers a1, a2, ..., an (0 ≤ ai ≤ 109) — elements of the array.

Output

If it's impossible to make all elements of the array equal using the process given in the problem statement, then print "NO" (without quotes) in the only line of the output. Otherwise print "YES" (without quotes).

Examples
input
51 3 3 2 1
output
YES
input
51 2 3 4 5
output
NO

Note

In the first sample Filya should select x = 1, then add it to the first and the last elements of the array and subtract from the second and the third elements.

题目大意：询问是否存在x能够令数组里一些数加上它一次或减去它一次或不作变化后数组里所有元素相等。

解题思路：最多有数组里有3种数才有可能实现，若多于3种数无论怎样最后都不能相等，然后剩下就是分类讨论的事了。

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