Seta is creating problems for the CCO! She came up with the following problem:
Given an array whose values are in the range , define to be the number of pairs such that and .
Print the array .
However, the day before the CCO, Seta’s computer crashed, and she was only able to recover the output files. Given the output array , can you write a program to reconstruct the input array ?
Seta reminds you that the array is not necessarily unique, and she will accept any valid array.
输入格式
The first line of input will contain a single integer, . The second line of input will contain space-separated integers ().
输出格式
Output space-separated integers, the array , where . It is guaranteed that there will always exist at least one valid array .
If there is more than one valid array, you may output any valid array. In particular, even if the original array is a permutation, your answer does not have to be a permutation.
样例
样例输入 1
3
3 1 2
样例输出 1
1 3 2
样例输入 2
2
2 2
样例输出 2
1 1
样例输入 3
3
1 4 1
样例输出 3
2 1 3
数据范围与提示
Explanation of Output for Sample Input
The subarrays , , have minimum . There are such subarrays.
The subarray has minimum . There is such subarray.
The subarrays and have minimum . There are such subarrays.
Explanation of Output for Sample Input
Note that would also be accepted by the judge.
The following table shows how the available marks are distributed:
