Here is a sequence a_1..n, which is a disordered sequence from 1 to N. if i < j and a_i > a_j, <i, j> is called a pair of inversion. And b_1..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.

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

5
2 1 2 0

3 1 4 2 5