There is a set of n segments with the lengths li. Find a segment with an integer length so that it could form a non-degenerate triangle with any two segments from the set, or tell that such segment doesn't exist.
The first line contains a single integer n (2 ≤ n ≤ 200000) — the number of segments in the set.
The second line contains n integers li separated by spaces (1 ≤ li ≤ 109) — the lengths of the segments in the set.
If the required segment exists, in the first line output «_YES_» (without quotes). In this case in the second line output a single integer x — the length of the needed segment. If there are many such segments, output any of them.
If the required segment doesn't exist, output «_NO_» (without quotes).
## Input
The first line contains a single integer n (2 ≤ n ≤ 200000) — the number of segments in the set.The second line contains n integers li separated by spaces (1 ≤ li ≤ 109) — the lengths of the segments in the set.
## Output
If the required segment exists, in the first line output «_YES_» (without quotes). In this case in the second line output a single integer x — the length of the needed segment. If there are many such segments, output any of them.If the required segment doesn't exist, output «_NO_» (without quotes).
[samples]
**Definitions**
Let $ n \in \mathbb{Z} $ be the number of segments, with $ 2 \leq n \leq 200000 $.
Let $ L = \{l_1, l_2, \dots, l_n\} $ be a multiset of positive integers representing the lengths of the segments, where $ 1 \leq l_i \leq 10^9 $.
**Constraints**
All $ l_i \in \mathbb{Z}^+ $.
**Objective**
Determine whether there exists an integer $ x \in \mathbb{Z}^+ $ such that for every pair of distinct segments $ l_i, l_j \in L $, the triple $ (l_i, l_j, x) $ forms a non-degenerate triangle.
That is, for all $ i \neq j $, the triangle inequalities hold:
$$
l_i + l_j > x, \quad l_i + x > l_j, \quad l_j + x > l_i.
$$
Equivalently, $ x $ must satisfy:
$$
x > \max_{i \neq j} \left( |l_i - l_j| \right) \quad \text{and} \quad x < \min_{i \neq j} (l_i + l_j).
$$
But since the condition must hold for **all pairs**, it suffices to require:
$$
x > \max_{1 \leq i < j \leq n} |l_i - l_j| = \max L - \min L,
$$
and
$$
x < \min_{1 \leq i < j \leq n} (l_i + l_j).
$$
Let $ M = \max L $, $ m = \min L $, and $ s = \min_{i \neq j} (l_i + l_j) $.
Then, such an integer $ x $ exists if and only if:
$$
M - m < s - 1,
$$
and in that case, any integer $ x \in (M - m,\, s) $ is valid (e.g., $ x = M - m + 1 $).
**Output**
If such $ x $ exists, output:
```
YES
x
```
Otherwise, output:
```
NO
```