Problem Statement

$N$ cards are arranged in a row from left to right. Each card either has $1$ positive integer written on it or has nothing written on it. The state of the $i$-th card from the left is represented by a non-negative integer $A_i$ as follows.

• If $A_i > 0$, the integer $A_i$ is written on the $i$-th card from the left.
• If $A_i = 0$, nothing is written on the $i$-th card from the left.

Now, consider performing the following operation on the cards.

• If there are cards with nothing written on them, write $1$ positive integer of your choice on each of them. Then, rearrange all the cards in any order you like (the order may be left as it is).

Let $B_i$ be the integer written on the $i$-th card from the left after the operation. Is it possible to perform the operation so that the sequence $B = (B_1, B_2, \ldots, B_N)$ is an arithmetic progression? That is, is it possible to perform the operation so that $B_2 - B_1 = B_3 - B_2 = \cdots = B_N - B_{N - 1}$ holds?

Input

$N$
$A_1$ $A_2$ $\ldots$ $A_N$

• All inputs are integers.
• $3 \leq N \leq 2 \times 10^5$
• $0 \leq A_i \leq 10^{15}$

Output

Print Yes if it is possible to perform the operation so that $B$ is an arithmetic progression, and No otherwise.

Sample

5
0 7 3 0 9

Yes

Sample

7
4 0 9 5 11 0 0

No

Sample

4
1 1 0 1

Yes