An n-element permutation is an n-element sequence of distinct numbers from the set {1, 2, ...,n}. For example the sequence 2, 1, 4, 5, 3 is a 5-element permutation. We are interested in the longest increasing subsequences in a permutation. In this exemplary permutation they are of length 3 and there are exactly 2 such subsequences: 2, 4, 5 and 1, 4, 5. We will call a number belonging to any of the longest increasing subsequences a supernumber. In the permutation 2, 1, 4, 5, 3 the supernumbers are 1, 2, 4, 5 and 3 is not a supernumber. Your task is to find all supernumbers for a given permutation.

Task

Write a program which

Input

Ten test cases (given one under another, you have to process all!). Each test case consists of two lines. In the first line there is a number n (1<=n<=100000). In the second line: an n-element permutation - n numbers separated by single spaces.

Output

For every test case your program should write two lines. In the first line - the number of supernumbers in the input permutation. In the second line the supernumbers separated by single spaces in increasing order.

Example

Input:
5
2 1 4 5 3
[and 9 test cases more]

Output:
4
1 2 4 5
[and 9 test cases more]