Median of Medians

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.

Constraints

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

Input

Input is given from Standard Input in the following format:

N a_1 a_2 ... a_N

Output

Print the median of m.

Examples

Input

3 10 30 20

Output

30

Input

1 10

Output

10

Input

10 5 9 5 9 8 9 3 5 4 3

Output

8

inputFormat

Input

Input is given from Standard Input in the following format:

N a_1 a_2 ... a_N

outputFormat

Output

Print the median of m.

Examples

Input

3 10 30 20

Output

30

Input

1 10

Output

10

Input

10 5 9 5 9 8 9 3 5 4 3

Output

8

样例

3
10 30 20

30