Every permutation A = (a₁, ..., a_n) of numbers 1, ..., n can be coded by a sequence B = (b₁, ..., b_n) in which b_i equals the number of all a_j such that (j < i & a_j > a_i), for i = 1, ..., n.

Example

Task

• reads from the text file KOD.IN 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 text file KOD.OUT,
• otherwise it writes in the file KOD.OUT one word NIE ("no").

Input

• In the first line of the text file KOD.IN there is a positive integer n <= 30000. 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 30000. It is the successive element of the sequence B.

Output

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

Examples

7
0
0
1
0
2
0
4

1
5
2
6
4
7
3

For the file KOD.IN:

4
0
2
0
0

NIE

Your program should look for the file KOD.IN in the current directory and create the file KOD.OUT also in the current directory. The source file containing the program written by you should be named KOD.???, where ??? are substituted by at most three-letter abbreviation of the programming language used. The same program in an executable form should be written in a file KOD.EXE.