Coding of Permutations

Memory limit: 32 MB

Every permutation of numbers can be coded by a sequence in which equals the number of all such that ( & ), for .

Example

The sequence is the code of the permutation .

Task

Write a program that:

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

Input

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

Output

The standard output should contain:

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

Examples

For the input data:

7
0
0
1
0
2
0
4

the correct result is:

1
5
2
6
4
7
3

For the input data:

4
0
2
0
0

the correct result is:

NIE

Task author: Krzysztof Diks.