A11767. Matrix Walk

There is a matrix $A$ of size $x×y$ filled with integers. For every ,  $A_{i,j}=y(i-1)+j$ . Obviously, every integer from $[1..xy]$ occurs exactly once in this matrix.

You have traversed some path in this matrix. Your path can be described as a sequence of visited cells $a_{1}$ , $a_{2}$ , ..., $a_{n}$ denoting that you started in the cell containing the number $a_{1}$ , then moved to the cell with the number $a_{2}$ , and so on.

From the cell located in $i$ -th line and $j$ -th column (we denote this cell as $(i,j)$ ) you can move into one of the following cells:

1. $(i+1,j)$ — only if $i<x$ ;
2. $(i,j+1)$ — only if $j<y$ ;
3. $(i-1,j)$ — only if $i>1$ ;
4. $(i,j-1)$ — only if $j>1$ .

Notice that making a move requires you to go to an adjacent cell. It is not allowed to stay in the same cell. You don't know $x$ and $y$ exactly, but you have to find any possible values for these numbers such that you could start in the cell containing the integer $a_{1}$ , then move to the cell containing $a_{2}$ (in one step), then move to the cell containing $a_{3}$ (also in one step) and so on. Can you choose $x$ and $y$ so that they don't contradict with your sequence of moves?

The first line contains one integer number $n$ ( $1<=n<=200000$ ) — the number of cells you visited on your path (if some cell is visited twice, then it's listed twice).

The second line contains $n$ integers $a_{1}$ , $a_{2}$ , ..., $a_{n}$ ( $1<=a_{i}<=10^{9}$ ) — the integers in the cells on your path.

If all possible values of $x$ and $y$ such that $1<=x,y<=10^{9}$ contradict with the information about your path, print NO.

Otherwise, print YES in the first line, and in the second line print the values $x$ and $y$ such that your path was possible with such number of lines and columns in the matrix. Remember that they must be positive integers not exceeding $10^{9}$ .

The matrix and the path on it in the first test looks like this:

Also there exist multiple correct answers for both the first and the third examples.