Problem:
Score : 400 points

Problem Statement

#nck {
width: 30px;
height: auto;
}

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.

Sample Input 1

2
1 2

Sample Output 1

1 4
5 4

a_1 + b_1 = 6 and a_2 + b_2 = 8. So this output satisfies all conditions.

Sample Input 2

3
3 2 1

Sample Output 2

1 2 3
5 3 1

Sample Input 3

3
2 3 1

Sample Output 3

5 10 100
100 10 1

Solution in Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc *bufio.Scanner

func nextStr() string {
	sc.Scan()
	return sc.Text()
}

func nextInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func main() {
	sc = bufio.NewScanner(os.Stdin)
	sc.Buffer(make([]byte, 0), 1000000001*3)
	sc.Split(bufio.ScanWords)
	n := nextInt()
	order := make([]int, n)
	for o := 1; o <= n; o++ {
		oi := nextInt()
		order[oi-1] = o
	}
	aArray, bArray := make([]int, n), make([]int, n)
	for i, o := range order {
		aArray[i] = n*i + o
		bArray[i] = n*(n-i-1) + o
	}
	for i, a := range aArray {
		fmt.Print(a)
		switch {
		case i == n-1:
			fmt.Println()
		default:
			fmt.Print(" ")
		}
	}
	for i, b := range bArray {
		fmt.Print(b)
		switch {
		case i == n-1:
			fmt.Println()
		default:
			fmt.Print(" ")
		}
	}
}