Jeff and Periods · Interview Problem

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Codeforces

Medium

Arrays

Hash Maps

Jeff and Periods

Find all values that appear in the array as a run of equal numbers whose total length matches the value itself.

Acceptance 0%

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Problem Statement

Problem

You are given an array of integers. A value is considered interesting if it appears in the array in one or more contiguous blocks, and the total number of times that value appears in the whole array is exactly equal to the value itself.

Your task is to output all interesting values in increasing order.

Clarification

If a number appears multiple times in different consecutive blocks, count all occurrences together. Only the final total frequency matters.

Goal

Identify every value $x$ such that the array contains exactly $x$ occurrences of $x$ .

Input Format

Input

The first line contains an integer $n$ — the size of the array.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ .

Output Format

Output

Print the number of interesting values.
Then print all interesting values in increasing order.

Constraints

$1 \le n \le 10^5$
$1 \le a_i \le 10^9$

Examples

Sample cases returned by the problem API.

Example 1

Input

7
4 5 4 5 4 5 5

Output

2
4 5

Explanation

The value 4 appears exactly 4 times, and the value 5 appears exactly 5 times. Both are interesting.

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