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문제

Every permutation A = (a1, ..., an) of numbers 1, ..., n can be coded by a sequence B = (b1, ..., bn) in which bi equals the number of all aj such that (j < i & aj > ai), for i = 1, ..., n.

The sequence B = (0, 0, 1, 0, 2, 0, 4) is the code of the permutation A = (1, 5, 2, 6, 4, 7, 3).

Write a program that:

  • reads from the standard input the length n and successive elements of the sequence B,
  • examines whether it is a code of some permutation of numbers 1, ..., n,
  • if so, it finds that permutation and writes it in the standard output,
  • otherwise it writes in the standard output one word NIE ("no").

입력

  • In the first line of the standard input there is a positive integer n ≤ 30,000. It is the number of elements of the sequence B.
  • In each of the following n lines there is one nonnegative integer not greater than 30,000. It is the successive element of the sequence B.

출력

The standard output should contain:

  • in each of n consecutive lines - one element of the permutation A, whose code is the sequence B written in the standard input,
  • one word NIE, if the sequence B is not a code of any permutation.

예제 입력 1

7
0
0
1
0
2
0
4

예제 출력 1

1
5
2
6
4
7
3

예제 입력 2

4
0
2
0
0

예제 출력 2

NIE