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A. Yaroslav and Permutations

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYaroslav has an array that consists of *n* integers. In one second Yaroslav can swap two neighboring array elements. Now Yaroslav is wondering if he can obtain an array where any two neighboring elements would be distinct in a finite time.

Help Yaroslav.

Input

The first line contains integer *n* (1 ≤ *n* ≤ 100) — the number of elements in the array. The second line contains *n* integers *a* _{1}, *a* _{2}, ..., *a* _{ n} (1 ≤ *a* _{ i} ≤ 1000) — the array elements.

Output

In the single line print "YES" (without the quotes) if Yaroslav can obtain the array he needs, and "NO" (without the quotes) otherwise.

Examples

Input

1

1

Output

YES

Input

3

1 1 2

Output

YES

Input

4

7 7 7 7

Output

NO

Note

In the first sample the initial array fits well.

In the second sample Yaroslav can get array: 1, 2, 1. He can swap the last and the second last elements to obtain it.

In the third sample Yarosav can't get the array he needs.

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