In a far far away land called the island of Zanzibar, Athena the Software Engineer is typing away on another problem. Earlier that day, her boss gave her ~N~ pizzas with tanginess values of ~a_1, a_2, \dots, a_N~, tasking her with finding two pizzas ~i~ and ~j~ such that ~i \ne j~ and ~|a_i+a_j|~ is minimized. But lately, Athena has been very swamped with physics lab work from the University of Waterloo writing boring business reports, and doesn't have time to complete the job. Can you help her finish it before the deadline?

Constraints

~2 \le N \le 10^6~

~-10^9 \le a_i \le 10^9~

Subtask 1 [10%]

~2 \le N \le 100~

Subtask 2 [90%]

No additional constraints.

Input Specification

The first line contains the integer ~N~.

The second line contains the space-separated integers ~a_1, a_2, \dots, a_N~.

Output Specification

Let ~A~ be the minimum possible value of ~|a_i+a_j|~ with the given input.

The first line should contain ~A~.

The second line should contain the space separated integers ~i, j~ such that ~|a_i+a_j|=A~. If there are multiple possible answers, output the one that minimizes ~10^7 \times i+j~.

Sample Input

10
-5 8 2 1 7 -3 -5 0 5 5

Sample Output

0
1 9

Sample Explanation

Taking the ~1^\text{st}~ and ~9^\text{th}~ pizzas results in the best possible sum of ~0~.