Let $A$ be a permutation of $1,2,\dots ,2N-1$.
We define the prefix medians of $A$ as an array $B$ with $N$ elements: where $B[i]$ is the median of $A[1],A[2],\dots ,A[2i-1]$.
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.

Task

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

Input Specification

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

Output Specification

The output should contain $A$: one line with $2N-1$ 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.

Constraints

• $1\le A[i]\le 2N-1$, for every $i$ from $1$ to $2N-1$
• $1\le B[i]\le 2N-1$, for every $i$ from $1$ to $N$
• $1\le N\le 100000$
• $60\mathrm{\%}$ of the tests will have $N\le 1000$

Sample Input

5
1 3 3 4 5

Sample Output

1 9 3 2 4 8 7 5 6