A choir director lines up n singers in a single row for a formation drill. Each singer has already been assigned a voice part: Alto or Soprano. The director wants to insert one imaginary divider somewhere along the row -- before the first singer, between any two adjacent singers, or after the last singer -- splitting the row into a left group and a right group (either group may be empty). For a divider placed at a given position, the formation's harmony score is defined as the number of Altos standing in the left group plus the number of Sopranos standing in the right group.

Find every divider position that achieves the maximum possible harmony score.

Input format

• Line 1: a single integer n, the number of singers.
• Line 2: n space-separated integers, the i-th being 0 if singer i is an Alto or 1 if singer i is a Soprano, in row order.

Output format

• A single line containing every divider position achieving the maximum harmony score, as space-separated integers in ascending order. A divider position is an integer p from 0 to n inclusive, meaning the left group consists of the first p singers and the right group consists of the remaining n - p singers.

Constraints

• 1 <= n <= 10^5
• each value is 0 or 1

4
0 0 1 0

2 4

3
0 0 0

3