Construct Sequences

You are given a permutation p of the set {1, 2, ..., N}. Please construct two sequences of positive integers a_1, a_2, ..., a_N and b_1, b_2, ..., b_N satisfying the following conditions:

• 1 \leq a_i, b_i \leq 10^9 for all i
• a_1 < a_2 < ... < a_N
• b_1 > b_2 > ... > b_N
• a_{p_1}+b_{p_1} < a_{p_2}+b_{p_2} < ... < a_{p_N}+b_{p_N}

Constraints

• 2 \leq N \leq 20,000
• p is a permutation of the set {1, 2, ..., N}

Input

The input is given from Standard Input in the following format:

N p_1 p_2 ... p_N

Output

The output consists of two lines. The first line contains a_1, a_2, ..., a_N seperated by a space. The second line contains b_1, b_2, ..., b_N seperated by a space.

It can be shown that there always exists a solution for any input satisfying the constraints.

Examples

Input

2 1 2

Output

1 4 5 4

Input

3 3 2 1

Output

1 2 3 5 3 1

Input

3 2 3 1

Output

5 10 100 100 10 1

inputFormat

Input

The input is given from Standard Input in the following format:

N p_1 p_2 ... p_N

outputFormat

Output

The output consists of two lines. The first line contains a_1, a_2, ..., a_N seperated by a space. The second line contains b_1, b_2, ..., b_N seperated by a space.

It can be shown that there always exists a solution for any input satisfying the constraints.

Examples

Input

2 1 2

Output

1 4 5 4

Input

3 3 2 1

Output

1 2 3 5 3 1

Input

3 2 3 1

Output

5 10 100 100 10 1

样例

3
3 2 1

1 2 3
5 3 1

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