Coding of Permutations

Every permutation $A = (a_1, \dots, a_n)$ of the numbers $1, \dots, n$ can be encoded by a sequence $B = (b_1, \dots, b_n)$, where $b_i$ is the number of indices $j$ with $j < i$ and $a_j > a_i$, for $i = 1, \dots, n$.

For example, 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 the length $n$ and the successive elements of the sequence $B$ from standard input,
• decides whether $B$ is the code of some permutation of the numbers $1, \dots, n$,
• if it is, finds that permutation and writes it to standard output,
• otherwise, writes the single word NIE ("no") to standard output.

• The first line of standard input contains a positive integer $n \le 30000$, the number of elements of the sequence $B$.
• Each of the following $n$ lines contains one nonnegative integer not greater than $30000$, giving the elements of the sequence $B$ in order.

Write the following to standard output:

• one element of the permutation $A$ per line, over $n$ consecutive lines, where $A$ is the permutation whose code is the sequence $B$ from the input,
• or the single word NIE if $B$ is not the code of any permutation.