As you know, escape rooms became very popular since they allow you to play the role of a video game hero. One such room has the following quiz. You know that the locker password is a permutation of N numbers. A permutation of length N is a sequence of distinct positive integers, whose values are at most N. You got the following hint regarding the password - the length of the longest increasing subsequence starting at position i equals A_i. Therefore you want to find the password using these values. As there can be several possible permutations you want to find the lexicographically smallest one. Permutation P is lexicographically smaller than permutation Q if there is an index i such that P_i < Q_i and P_j = Q_j for all j < i. It is guaranteed that there is at least one possible permutation satisfying the above constraints. Can you open the door?

입력 형식

The first line of the input contains one integer N (1 ≤ N ≤ 10⁵).</p>

The next line contains N space-separated integer A_i (1 ≤ A_i ≤ N).

It’s guaranteed that at least one possible permutation exists. 

출력 형식

Print in one line the lexicographically smallest permutation that satisfies all the conditions.

예제 입력 1

4
1 2 2 1

예제 출력 1

4 2 1 3

예제 입력 2

1
1

예제 출력 2

1