Element Closest to the Average (Phần tử gần trung bình nhất)

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem

Given integers $a_0,\ldots,a_{n-1}$, define

Choose the smallest index $p$ minimizing $|a_p-\mu|$. Equivalently, with $S=\sum a_i$, compare

using integer arithmetic. Print $p$ and $a_p$.

Input

The first line contains $n$. The second line contains $n$ integers $a_i$.

Output

Print p a_p, where $p$ is the selected 0-based index.

Subtask

Subtask 1 (20 points): $1\le n\le10$, $|a_i|\le10^3$.

Subtask 2 (30 points): $1\le n\le5000$, $|a_i|\le10^6$.

Subtask 3 (50 points): $1\le n\le2\cdot10^5$, $|a_i|\le10^9$.

Example

Input

5
1 4 8 10 12

Output

2 8

Explanation

The sample follows the definitions and rules above.