There is a matrix A of size x × y filled with integers. For every $\text{[math]}$ , $\text{[math]}$ 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 a₁, a₂, ..., a_n denoting that you started in the cell containing the number a₁, then moved to the cell with the number a₂, 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:

(i + 1, j) — only if i < x;
(i, j + 1) — only if j < y;
(i - 1, j) — only if i > 1;
(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 a₁, then move to the cell containing a₂ (in one step), then move to the cell containing a₃ (also in one step) and so on. Can you choose x and y so that they don't contradict with your sequence of moves?

Input

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 a₁, a₂, ..., a_n (1 ≤ a_i ≤ 10⁹) — the integers in the cells on your path.

Output

If all possible values of x and y such that 1 ≤ x, y ≤ 10⁹ 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 10⁹.

Note

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

$\text{[math]}$

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

Matrix Walk

Examples