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문제

Let A be a permutation of 1, 2, 3 ..., 2*N - 1.

We define the prefix medians of A as an array B with N elements: where B[i] is the median of A[1], A[2], ..., A[2*i-1].

Note: The median of a list of M numbers (where M is odd) can be found by sorting the numbers and picking the middle one.

You are given N and the array B. You are asked to determine a permutation A whose prefix medians are precisely B.

입력

The input file contains 2 lines. The first line contains one integer, N. The second line describes B: N integers, separated by space.

Constraints

  • 1 ≤ A[i] ≤ 2*N - 1, for every i from 1 to 2*N - 1
  • 1 ≤ B[i] ≤ 2*N - 1, for every i from 1 to N
  • 1 ≤ N ≤ 100 000
  • 60% of the tests will have N ≤ 1000

출력

The output file should contain A: one line with 2*N-1 integers separated by space. If there are multiple permutations A leading to the same input array B, you may output any one. In all test data, there will always be at least one solution.

예제 입력 1

5
1 3 3 4 5

예제 출력 1

1 9 3 2 4 8 7 5 6