시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
3 초 256 MB 0 0 0 0.000%

## 문제

Two functions f and g (f, g : X → X) are commuting if and only if f(g(x)) = g(f(x)) for each x ∈ X. For example, functions f(x) = x + 1 and g(x) = x − 2 are commuting, whereas functions f(x) = x + 1 and g(x) = 2x are not commuting.

Each function h (h : Nn → Nn, where Nn = 1, 2, . . . , n and n is positive integer) can be represented as a value list — a list in which the i-th element is equal to h(i). For example, a function h(x) = ⌈x/2⌉ from N5 to N5 has the value list [1, 1, 2, 2, 3].

The value lists are ordered lexicographically: list [a1 . . . an] is smaller than list [b1 . . . bn] if and only if there exists such an index k that ak < bk, and al = bl for any index l < k.

The function f (f : X → X) is bijective if for every y in X, there is exactly one x in X such that f(x) = y.

Given a bijective function f (f : Nn → Nn, n is positive integer), find the function g that is commuting with f and has the lexicographically smallest possible value list.

## 입력

The first line contains single integer number n — the number of the elements in the value list of bijective function f (1 ≤ n ≤ 200 000).

The second line of the input file contains the value list of the function f.

## 출력

The single line of the output file must contain n integer numbers — the value list of function g that commutes with the function f and has the lexicographically smallest value list.

## 예제 입력 1

10
1 2 3 4 5 6 7 8 9 10


## 예제 출력 1

1 1 1 1 1 1 1 1 1 1


## 예제 입력 2

10
2 3 4 5 6 7 8 1 9 10


## 예제 출력 2

1 2 3 4 5 6 7 8 9 9