Histogram Reordering

Limits 1s, 512 MB

You are given an array of integers HH, representing the height of the bars of a histogram. The width of each bar is 1. Now you will reorder the bars in such a way that the largest area of a rectangle in your histogram is the maximum possible amongst all possible reorderings.

You need to print a reordering of the histogram that satisfies the given condition. A reordering is a permutation of indexes from 11 to nn where nn is the size of the array. If there are multiple possible answers, you have to print the lexicographically smallest permutation.

See the sample description for a better understanding.


Input starts with an integer T(1T105)T( 1 \leq T \leq 10^5),

Each testcase starts with an integer n(1n105)n( 1 \leq n \leq 10^5), the size of the array HH.

The next line contains nn space-separated integers, H1,H2,,Hn(1Hi106)H_1, H_2, \dots, H_n(1 \leq H_i \leq 10^6)

Sum of nn in all the test cases don’t exceed 10610^6.


For each testcase print nn integers in a line, the reordering of the histogram that satisfies the given condition.


7 2
5 3 7
1 2
1 3 2

In test case 1:

There are two possible reorderings(shown in the picture, black rectangle indicates the largest rectangle)
If you use the ordering {1, 2}, the histogram stays {7, 2} which has a maximum rectangular area of 7 units.

If you use the ordering {2, 1}, the histogram becomes {2, 7} which also has a maximum rectangle of 7 units.

Between the orderings, {1, 2} is lexicographically smaller.

In test case 2:

There are 6 possible reorderings(3 of those are shown in the picture), Among the orderings {1, 3, 2}, {3, 1, 2}, {2, 1, 3}, {2, 3, 1} all have a maximum rectangular area of 10 and the ordering {1, 3, 2} is the lexicographically smallest one.