8120번 - Coding of Permutations 다국어

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.

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").

• 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.

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.