Problem Statement

We will define the median of a sequence b of length M, as follows:

• Let b' be the sequence obtained by sorting b in non-decreasing order. Then, the value of the (M / 2 + 1)-th element of b' is the median of b. Here, / is integer division, rounding down.

For example, the median of (10, 30, 20) is 20; the median of (10, 30, 20, 40) is 30; the median of (10, 10, 10, 20, 30) is 10.
Snuke comes up with the following problem.
You are given a sequence a of length N.
For each pair $(l, r) (1 \leq l \leq r \leq N)$, let m_{l, r} be the median of the contiguous subsequence (a_l, a_{l + 1}, ..., a_r) of a.
We will list m_{l, r} for all pairs (l, r) to create a new sequence m.
Find the median of m.

Input

Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N

Output

Print the median of m.

Constraints

• $1 \leq N \leq 10^5$
• a_i is an integer.
• $1 \leq a_i \leq 10^9$

Sample Input 1

3
10 30 20

Sample Output 1

30

The median of each contiguous subsequence of a is as follows:

• The median of (10) is 10.
• The median of (30) is 30.
• The median of (20) is 20.
• The median of (10, 30) is 30.
• The median of (30, 20) is 30.
• The median of (10, 30, 20) is 20.

Thus, m = (10, 30, 20, 30, 30, 20) and the median of m is 30.

Sample Input 2

1
10

Sample Output 2

10

Sample Input 3

10
5 9 5 9 8 9 3 5 4 3

Sample Output 3

8

见题面 Input 部分

见题面 Output 部分