1434 - reverse order 2

Time Limit : 1 Second

Memory Limit : 128 MB

Submission: 179

Solved: 72

Description


Here is a sequence a1..n, which is a disordered sequence from 1 to N. if i < j and ai > aj, <i, j> is called a pair of inversion. And b1..n-1 is defined as follows, bk is the number of the total inversion pairs in array a, when i<=k<j. Now the array a is required while the array b is known.


Input


 



Several cases end with the end of the file;



And each of the cases includes two lines, a integer n(2<=n<=10^5)in the first line, and the second line followed with n-1 integer, which is in the presentation of array b;


Output


Output the answer of each case in a line, namely the array a, and a space is required between adjacent integers.


sample input
5
2 1 2 0
sample output
3 1 4 2 5
hint
source
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