As an employee of the Amaze-Combines-with-Magicpig(ACM) company, Kinfkong has been asked to store some integer keys. The keys must be stored in a special ordered collection that can be considered as an array A, which has an infinite number of locations, numbered starting from 1. Initially all locations are empty. The following operation must be supported by the collection: Insert(L, K), where L is the location in the array and K is a positive integer value.

The operation must be processed as follows:

If A[L] is empty, set A[L] <- K.
If A[L] is not empty, perform Insert(L + 1, K).

These days Kinfkong is too busy, so he asks you to help him!
Given N integer numbers L1 , L2 , . . . , LN, you have to output the contents of the array after a sequence of the following operations:

Insert(L1 , 1)
Insert(L2 , 2)
. . .
Insert(LN , N)

The first line of the input file contains N --- the number of Insert operations (1 <= N <= 100000).
Next line contains N integer numbers Li that describe Insert operations to be performed (1 <= Li <= N ).
A line which contains a single 0 will end the input.

Output the contents of the array after a given sequence of Insert operations. On the first line print W --- the number of the greatest location that is not empty. After that output W integer numbers --- A[1], A[2], . . . , A[W] ,separated by a single space. Output zeroes for empty locations.

Sample Input

3 3 4 1 3

Sample Output

4 0 1 2 3 5


Author: Mathematica