Pyramid

Limits: 2 sec., 256 MiB

This statement was translated automatically from Ukrainian.

Zenyk has \(n\) sticks with lengths \(a_i\).

We will consider that \(k\) sticks with lengths \(x_1\), \(x_2\), ..., \(x_k\) form a pyramid if, by rearranging them, one can obtain a set of \(k\) sticks with lengths 1, 3, 5, ..., \(2k - 1\).

The width of a pyramid is defined as the length of its longest stick.

Zenyk can decrease the lengths of arbitrary sticks from the set.

Help Zenyk — tell what is the maximum width of a pyramid that can be obtained using the sticks from the set.

Input

The first line contains an integer \(n\) — the number of sticks in the set.

The second line contains \(n\) integers — the lengths of the sticks in the set.

Output

Print a single integer in one line — the answer to the problem.

Constraints

\(1 \le n \le 10^5\),

\(1 \le a_i \le 10^9\).

Samples

Input (stdin) сopy	Output (stdout) сopy
6 1 23 4 8 7 3	9

Notes

Note that Zenyk can use not all sticks to build the pyramid.