Consider a permutation of the first $N$ positive integers, $p_1,p_2,\dots ,p_N$. Define $a_i$ as the length of the longest increasing subsequence of $p_1,p_2,\dots ,p_i$.

Given $a_1,a_2,\dots ,a_n$, find the lexicographically minimal possible permutation $p_1,p_2,\dots ,p_N$, or determine that no such permutation exists.

Constraints

$1\le N\le 2\times {10}^5$

$1\le a_i\le N$

Input Specification

The first line contains an integer, $N$.

The second line contains $N$ space-separated integers, $a_1,a_2,\dots ,a_N$.

Output Specification

If there is no sequence $p$ that can produce sequence $a$, output $-1$; otherwise, output one line containing $N$ positive integers, representing the lexicographically minimal permutation $p_1,p_2,\dots ,p_N$.

Sample Input 1

3
1 2 2

Sample Output 1

1 3 2

Explanation for Sample Output 1

Note that

• The longest increasing subsequence of $p_1$ is $1$.
• The longest increasing subsequence of $p_1,p_2$ is $1,3$.
• One of the longest increasing subsequences of $p_1,p_2,p_3$ is $1,2$.

Sample Input 2

3
1 2 1

Sample Output 2

-1

Explanation for Sample Output 2

No possible permutation $p$ exists.