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.