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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>

#ifdef WIN32
	#define LL "%I64d"
#else
	#define LL "%lld"
#endif

#ifdef CT
	#define debug(...) printf(__VA_ARGS__)
	#define setfile() 
#else
	#define debug(...)
	#define filename ""
	#define setfile() freopen(filename".in", "r", stdin); freopen(filename".out", "w", stdout)
#endif

#define R register
#define getc() (S == T && (T = (S = B) + fread(B, 1, 1 << 15, stdin), S == T) ? EOF : *S++)
#define dmax(_a, _b) ((_a) > (_b) ? (_a) : (_b))
#define dmin(_a, _b) ((_a) < (_b) ? (_a) : (_b))
#define cmax(_a, _b) (_a < (_b) ? _a = (_b) : 0)
#define cmin(_a, _b) (_a > (_b) ? _a = (_b) : 0)
#define cabs(_x) ((_x) < 0 ? (- (_x)) : (_x))
char B[1 << 15], *S = B, *T = B;
inline int F()
{
	R char ch; R int cnt = 0; R bool minus = 0;
	while (ch = getc(), (ch < '0' || ch > '9') && ch != '-') ;
	ch == '-' ? minus = 1 : cnt = ch - '0';
	while (ch = getc(), ch >= '0' && ch <= '9') cnt = cnt * 10 + ch - '0';
	return minus ? -cnt : cnt;
}
#define maxn 20010
int p[maxn], a[maxn], b[maxn];
int main()
{
//	setfile();
	int n = F();
	for (int i = 0; i < n; ++i) p[i] = F();
	a[1] = 1;
	for (int i = 2; i <= n; ++i) a[i] = a[i - 1] + n;
	for (int i = n; i; --i) b[i] = a[n - i + 1];
	for (int i = 0; i < n; ++i) a[p[i]] += i;

	for (int i = 1; i <= n; ++i) printf("%d ", a[i] ); puts("");
	for (int i = 1; i <= n; ++i) printf("%d ", b[i] ); puts("");
	return 0;
}