시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

마오공 곤돌라는 타이페이의 명소 중 하나이다. 곤돌라 시스템은 원형의 레일과, 하나의 정류장이 있고, 1 부터 n까지 순서대로 번호가 붙은 n개의 곤돌라가 모두 단일한 방향으로 레일을 따라 움직이는 형태이다. i번 곤돌라가 정류장을 지난 직후에는 i+1번 곤돌라가 정류장을 지나가게 된다. (단, i=n번 곤돌라가 지나간 직후에 1 번 곤돌라가 지나가게 된다.)

곤돌라들은 고장이 나기도 한다. 다행히 무제한으로 많은 곤돌라의 여분이 있고, 여분 곤돌라들은 n+1, n+2과 같이 순차적으로 번호가 붙어 있다. 특정한 곤돌라가 고장이 나면 고장난 곤돌라는 빼고, 동일한 위치에 여분 곤돌라를 배치한다. 여분 곤돌라는 작은 번호부터 사용된다. 예를 들어, 사용하는 곤돌라 수가 총 5 개이고, 1 번 곤돌라가 고장난다면, 그 곤돌라는 6번으로 교체된다.

당신은 정류장에 서서 곤돌라들이 지나가는 것을 즐겨 본다. 곤돌라 수열이라는 것은 임의의 시점에서 시작해서 정류장을 지나가는 n개의 곤돌라들의 번호를 순서대로 적은 것이다. 곤돌라 수열을 적기 시작하는 시점 이전에 이미 몇개의 곤돌라가 고장나서 교체되었을 수 있다. 하지만, 곤돌라 수열을 적는 도중에는 아무 곤돌라도 고장이 나지 않는다.

전체적으로 곤돌라들의 배치가 동일하더라도 어떤 시점에 곤돌라 수열을 적기 시작하느냐에 따라 서로 다른 곤돌라 수열이 나올수 있다는 점에 주의하자. 예를 들어, 총 5개의 곤돌라들 중 고장난 곤돌라가 없는 경우에 (2, 3, 4, 5, 1) 과 (4, 5, 1, 2, 3) 은 모두 가능한 곤돌라 수열들이다. 하지만, 이경우 (4, 3, 2, 5, 1) 은 가능한 곤돌라 수열이 아니다. (곤돌라 번호의 순서가 잘못되어 있다.)

만약 곤돌라 1번 만이 고장난 상황이라면, (4, 5, 6, 2, 3) 의 곤돌라 수열을 만들 수 있다. 만약 이후 4번 곤돌라가 고장난다면, 7번 곤돌라가 그 자리에 있게 되고, (6, 2, 3, 7, 5) 가 가능한 곤돌라 수열이 된다. 만약 7번 곤돌라가 이후에 고장이 난다면, 8번이 그 자리를 차지할 것이고 (3, 8, 5, 6, 2) 가 가능한 곤돌라 수열들 중 하나가 된다.

고장난 곤돌라 새 곤돌라 가능한 곤돌라 수열 중 하나
1 6 (4, 5, 6, 2, 3)
4 7 (6, 2, 3, 7, 5)
7 8 (3, 8, 5, 6, 2)

교체 수열이라는 것은 고장난 곤돌라들의 번호를 고장난 순서에 따라 쓴 것이다. 직전의 예에서 교체 수열은 (1, 4, 7) 이다. 교체 수열 e이 곤돌라 수열 g를 만든다고 말을 할 수 있는데, 그것은 초기 상황에서 시작해서 r에 해당하는 방법으로 곤돌라들이 고장난 직후에, g가 가능한 곤돌라 수열들 중 하나인 경우를 의미한다.

이 문제에서는 주어진 수열(가능한 곤돌라 수열일 수도 아닐 수도 있음)을 만들 수 있는 교체 수열의 수를 세어서 그 값을 1,000,000,009 로 나눈 나머지를 계산해야 한다. 다음과 같이 선언된 함수 countReplacement 를 구현해야 한다.

  • countReplacement(n, inputSeq)
    • n: 입력 수열의 길이.
    • inputSeq: 크기 인 배열; inputSeq[i]는 입력 수열의 번 원소이다 (0 ≤ i ≤ n-1).
    • 입력이 곤돌라 수열인 경우, 입력의 곤돌라 수열을 만들 수 있는 모든 교체 수열의 수를 센 다음에 (그 수는 매우 클수 있음) 그 결과를 1,000,000,009 로 나눈 나머지를 리턴해야 한다. 만약 입력이 곤돌라 수열이 아닌 경우 0을 리턴해야 한다. 입력이 곤돌라 수열이고 고장난 곤돌라가 하나도 없는 경우는 1을 리턴해야 한다.

입력

첫째 줄에 입력 수열의 길이 n이 주어진다. (1 ≤ n ≤ 100,000)

둘째 줄에는 inputSeq[0], ..., inputSeq[n-1]이 주어진다. (1 ≤ inputSeq[i] ≤ 1,000,000,000)

출력

countReplacement함수의 리턴값을 출력한다.

예제 입력 1

4
1 2 7 6

예제 출력 1

2

힌트

inputSeq 리턴 값 교체 수열
(1, 2, 7, 6) 2 (3, 4, 5) or (4, 5, 3)
(2, 3, 4, 12, 6, 7, 1) 1 (5, 8, 9, 10, 11)
(4, 7, 4, 7) 0 inputSeq가 곤돌라 수열이 아님
(3, 4) 2 (1, 2) or (2, 1)
[{"problem_id":"10074","problem_lang":"0","title":"\uace4\ub3cc\ub77c - \uad50\uccb4 \uc218\uc5f4\uc758 \uac1c\uc218 \uc138\uae30","description":"<p>\ub9c8\uc624\uacf5 \uace4\ub3cc\ub77c\ub294 \ud0c0\uc774\ud398\uc774\uc758 \uba85\uc18c \uc911 \ud558\ub098\uc774\ub2e4. \uace4\ub3cc\ub77c \uc2dc\uc2a4\ud15c\uc740 \uc6d0\ud615\uc758 \ub808\uc77c\uacfc, \ud558\ub098\uc758 \uc815\ub958\uc7a5\uc774 \uc788\uace0, 1 \ubd80\ud130 n\uae4c\uc9c0 \uc21c\uc11c\ub300\ub85c \ubc88\ud638\uac00 \ubd99\uc740 n\uac1c\uc758 \uace4\ub3cc\ub77c\uac00 \ubaa8\ub450 \ub2e8\uc77c\ud55c \ubc29\ud5a5\uc73c\ub85c \ub808\uc77c\uc744 \ub530\ub77c \uc6c0\uc9c1\uc774\ub294 \ud615\ud0dc\uc774\ub2e4. i\ubc88 \uace4\ub3cc\ub77c\uac00 \uc815\ub958\uc7a5\uc744 \uc9c0\ub09c \uc9c1\ud6c4\uc5d0\ub294 i+1\ubc88 \uace4\ub3cc\ub77c\uac00 \uc815\ub958\uc7a5\uc744 \uc9c0\ub098\uac00\uac8c \ub41c\ub2e4. (\ub2e8, i=n\ubc88 \uace4\ub3cc\ub77c\uac00 \uc9c0\ub098\uac04 \uc9c1\ud6c4\uc5d0 1 \ubc88 \uace4\ub3cc\ub77c\uac00 \uc9c0\ub098\uac00\uac8c \ub41c\ub2e4.)<\/p>\r\n\r\n<p>\uace4\ub3cc\ub77c\ub4e4\uc740 \uace0\uc7a5\uc774 \ub098\uae30\ub3c4 \ud55c\ub2e4. \ub2e4\ud589\ud788 \ubb34\uc81c\ud55c\uc73c\ub85c \ub9ce\uc740 \uace4\ub3cc\ub77c\uc758 \uc5ec\ubd84\uc774 \uc788\uace0, \uc5ec\ubd84 \uace4\ub3cc\ub77c\ub4e4\uc740 n+1, n+2\uacfc \uac19\uc774 \uc21c\ucc28\uc801\uc73c\ub85c \ubc88\ud638\uac00 \ubd99\uc5b4 \uc788\ub2e4. \ud2b9\uc815\ud55c \uace4\ub3cc\ub77c\uac00 \uace0\uc7a5\uc774 \ub098\uba74 \uace0\uc7a5\ub09c \uace4\ub3cc\ub77c\ub294 \ube7c\uace0, \ub3d9\uc77c\ud55c \uc704\uce58\uc5d0 \uc5ec\ubd84 \uace4\ub3cc\ub77c\ub97c \ubc30\uce58\ud55c\ub2e4. \uc5ec\ubd84 \uace4\ub3cc\ub77c\ub294 \uc791\uc740 \ubc88\ud638\ubd80\ud130 \uc0ac\uc6a9\ub41c\ub2e4. \uc608\ub97c \ub4e4\uc5b4, \uc0ac\uc6a9\ud558\ub294 \uace4\ub3cc\ub77c \uc218\uac00 \ucd1d 5 \uac1c\uc774\uace0, 1 \ubc88 \uace4\ub3cc\ub77c\uac00 \uace0\uc7a5\ub09c\ub2e4\uba74, \uadf8 \uace4\ub3cc\ub77c\ub294 6\ubc88\uc73c\ub85c \uad50\uccb4\ub41c\ub2e4.<\/p>\r\n\r\n<p>\ub2f9\uc2e0\uc740 \uc815\ub958\uc7a5\uc5d0 \uc11c\uc11c \uace4\ub3cc\ub77c\ub4e4\uc774 \uc9c0\ub098\uac00\ub294 \uac83\uc744 \uc990\uaca8 \ubcf8\ub2e4. \uace4\ub3cc\ub77c \uc218\uc5f4\uc774\ub77c\ub294 \uac83\uc740 \uc784\uc758\uc758 \uc2dc\uc810\uc5d0\uc11c \uc2dc\uc791\ud574\uc11c \uc815\ub958\uc7a5\uc744 \uc9c0\ub098\uac00\ub294 n\uac1c\uc758 \uace4\ub3cc\ub77c\ub4e4\uc758 \ubc88\ud638\ub97c \uc21c\uc11c\ub300\ub85c \uc801\uc740 \uac83\uc774\ub2e4. \uace4\ub3cc\ub77c \uc218\uc5f4\uc744 \uc801\uae30 \uc2dc\uc791\ud558\ub294 \uc2dc\uc810 \uc774\uc804\uc5d0 \uc774\ubbf8 \uba87\uac1c\uc758 \uace4\ub3cc\ub77c\uac00 \uace0\uc7a5\ub098\uc11c \uad50\uccb4\ub418\uc5c8\uc744 \uc218 \uc788\ub2e4. \ud558\uc9c0\ub9cc, \uace4\ub3cc\ub77c \uc218\uc5f4\uc744 \uc801\ub294 \ub3c4\uc911\uc5d0\ub294 \uc544\ubb34 \uace4\ub3cc\ub77c\ub3c4 \uace0\uc7a5\uc774 \ub098\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n\r\n<p>\uc804\uccb4\uc801\uc73c\ub85c \uace4\ub3cc\ub77c\ub4e4\uc758 \ubc30\uce58\uac00 \ub3d9\uc77c\ud558\ub354\ub77c\ub3c4 \uc5b4\ub5a4 \uc2dc\uc810\uc5d0 \uace4\ub3cc\ub77c \uc218\uc5f4\uc744 \uc801\uae30 \uc2dc\uc791\ud558\ub290\ub0d0\uc5d0 \ub530\ub77c \uc11c\ub85c \ub2e4\ub978 \uace4\ub3cc\ub77c \uc218\uc5f4\uc774 \ub098\uc62c\uc218 \uc788\ub2e4\ub294 \uc810\uc5d0 \uc8fc\uc758\ud558\uc790. \uc608\ub97c \ub4e4\uc5b4, \ucd1d 5\uac1c\uc758 \uace4\ub3cc\ub77c\ub4e4 \uc911 \uace0\uc7a5\ub09c \uace4\ub3cc\ub77c\uac00 \uc5c6\ub294 \uacbd\uc6b0\uc5d0 (2, 3, 4, 5, 1) \uacfc (4, 5, 1, 2, 3) \uc740 \ubaa8\ub450 \uac00\ub2a5\ud55c \uace4\ub3cc\ub77c \uc218\uc5f4\ub4e4\uc774\ub2e4. \ud558\uc9c0\ub9cc, \uc774\uacbd\uc6b0 (4, 3, 2, 5, 1) \uc740 \uac00\ub2a5\ud55c \uace4\ub3cc\ub77c \uc218\uc5f4\uc774 \uc544\ub2c8\ub2e4. (\uace4\ub3cc\ub77c \ubc88\ud638\uc758 \uc21c\uc11c\uac00 \uc798\ubabb\ub418\uc5b4 \uc788\ub2e4.)<\/p>\r\n\r\n<p>\ub9cc\uc57d \uace4\ub3cc\ub77c 1\ubc88 \ub9cc\uc774 \uace0\uc7a5\ub09c \uc0c1\ud669\uc774\ub77c\uba74, (4, 5, 6, 2, 3) \uc758 \uace4\ub3cc\ub77c \uc218\uc5f4\uc744 \ub9cc\ub4e4 \uc218 \uc788\ub2e4. \ub9cc\uc57d \uc774\ud6c4 4\ubc88 \uace4\ub3cc\ub77c\uac00 \uace0\uc7a5\ub09c\ub2e4\uba74, 7\ubc88 \uace4\ub3cc\ub77c\uac00 \uadf8 \uc790\ub9ac\uc5d0 \uc788\uac8c \ub418\uace0, (6, 2, 3, 7, 5) \uac00 \uac00\ub2a5\ud55c \uace4\ub3cc\ub77c \uc218\uc5f4\uc774 \ub41c\ub2e4. \ub9cc\uc57d 7\ubc88 \uace4\ub3cc\ub77c\uac00 \uc774\ud6c4\uc5d0 \uace0\uc7a5\uc774 \ub09c\ub2e4\uba74, 8\ubc88\uc774 \uadf8 \uc790\ub9ac\ub97c \ucc28\uc9c0\ud560 \uac83\uc774\uace0 (3, 8, 5, 6, 2) \uac00 \uac00\ub2a5\ud55c \uace4\ub3cc\ub77c \uc218\uc5f4\ub4e4 \uc911 \ud558\ub098\uac00 \ub41c\ub2e4.<\/p>\r\n\r\n<table class=\"table table-bordered\" style=\"width:40%\">\r\n\t<thead>\r\n\t\t<tr>\r\n\t\t\t<th>\uace0\uc7a5\ub09c \uace4\ub3cc\ub77c<\/th>\r\n\t\t\t<th>\uc0c8 \uace4\ub3cc\ub77c<\/th>\r\n\t\t\t<th>\uac00\ub2a5\ud55c \uace4\ub3cc\ub77c \uc218\uc5f4 \uc911 \ud558\ub098<\/th>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t<\/tr>\r\n\t<\/thead>\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>6<\/td>\r\n\t\t\t<td>(4, 5, 6, 2, 3)<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>4<\/td>\r\n\t\t\t<td>7<\/td>\r\n\t\t\t<td>(6, 2, 3, 7, 5)<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>7<\/td>\r\n\t\t\t<td>8<\/td>\r\n\t\t\t<td>(3, 8, 5, 6, 2)<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n\r\n<p>\uad50\uccb4 \uc218\uc5f4\uc774\ub77c\ub294 \uac83\uc740 \uace0\uc7a5\ub09c \uace4\ub3cc\ub77c\ub4e4\uc758 \ubc88\ud638\ub97c \uace0\uc7a5\ub09c \uc21c\uc11c\uc5d0 \ub530\ub77c \uc4f4 \uac83\uc774\ub2e4. \uc9c1\uc804\uc758 \uc608\uc5d0\uc11c \uad50\uccb4 \uc218\uc5f4\uc740 (1, 4, 7) \uc774\ub2e4. \uad50\uccb4 \uc218\uc5f4 e\uc774 \uace4\ub3cc\ub77c \uc218\uc5f4 g\ub97c \ub9cc\ub4e0\ub2e4\uace0 \ub9d0\uc744 \ud560 \uc218 \uc788\ub294\ub370, \uadf8\uac83\uc740 \ucd08\uae30 \uc0c1\ud669\uc5d0\uc11c \uc2dc\uc791\ud574\uc11c r\uc5d0 \ud574\ub2f9\ud558\ub294 \ubc29\ubc95\uc73c\ub85c \uace4\ub3cc\ub77c\ub4e4\uc774 \uace0\uc7a5\ub09c \uc9c1\ud6c4\uc5d0, g\uac00 \uac00\ub2a5\ud55c \uace4\ub3cc\ub77c \uc218\uc5f4\ub4e4 \uc911 \ud558\ub098\uc778 \uacbd\uc6b0\ub97c \uc758\ubbf8\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc774 \ubb38\uc81c\uc5d0\uc11c\ub294 \uc8fc\uc5b4\uc9c4 \uc218\uc5f4(\uac00\ub2a5\ud55c \uace4\ub3cc\ub77c \uc218\uc5f4\uc77c \uc218\ub3c4 \uc544\ub2d0 \uc218\ub3c4 \uc788\uc74c)\uc744 \ub9cc\ub4e4 \uc218 \uc788\ub294 \uad50\uccb4 \uc218\uc5f4\uc758 \uc218\ub97c \uc138\uc5b4\uc11c \uadf8 \uac12\uc744 1,000,000,009 \ub85c \ub098\ub208 \ub098\uba38\uc9c0\ub97c \uacc4\uc0b0\ud574\uc57c \ud55c\ub2e4. \ub2e4\uc74c\uacfc \uac19\uc774 \uc120\uc5b8\ub41c \ud568\uc218 countReplacement \ub97c \uad6c\ud604\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>countReplacement(n, inputSeq)\r\n\t<ul>\r\n\t\t<li>n: \uc785\ub825 \uc218\uc5f4\uc758 \uae38\uc774.<\/li>\r\n\t\t<li>inputSeq: \ud06c\uae30 \uc778 \ubc30\uc5f4; inputSeq[i]\ub294 \uc785\ub825 \uc218\uc5f4\uc758 \ubc88 \uc6d0\uc18c\uc774\ub2e4 (0 &le; i &le; n-1).<\/li>\r\n\t\t<li>\uc785\ub825\uc774 \uace4\ub3cc\ub77c \uc218\uc5f4\uc778 \uacbd\uc6b0, \uc785\ub825\uc758 \uace4\ub3cc\ub77c \uc218\uc5f4\uc744 \ub9cc\ub4e4 \uc218 \uc788\ub294 \ubaa8\ub4e0 \uad50\uccb4 \uc218\uc5f4\uc758 \uc218\ub97c \uc13c \ub2e4\uc74c\uc5d0 (\uadf8 \uc218\ub294 \ub9e4\uc6b0 \ud074\uc218 \uc788\uc74c) \uadf8 \uacb0\uacfc\ub97c 1,000,000,009 \ub85c \ub098\ub208 \ub098\uba38\uc9c0\ub97c \ub9ac\ud134\ud574\uc57c \ud55c\ub2e4. \ub9cc\uc57d \uc785\ub825\uc774 \uace4\ub3cc\ub77c \uc218\uc5f4\uc774 \uc544\ub2cc \uacbd\uc6b0 0\uc744 \ub9ac\ud134\ud574\uc57c \ud55c\ub2e4. \uc785\ub825\uc774 \uace4\ub3cc\ub77c \uc218\uc5f4\uc774\uace0 \uace0\uc7a5\ub09c \uace4\ub3cc\ub77c\uac00 \ud558\ub098\ub3c4 \uc5c6\ub294 \uacbd\uc6b0\ub294 1\uc744 \ub9ac\ud134\ud574\uc57c \ud55c\ub2e4.<\/li>\r\n\t<\/ul>\r\n\t<\/li>\r\n<\/ul>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc785\ub825 \uc218\uc5f4\uc758 \uae38\uc774 n\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; n &le; 100,000)<\/p>\r\n\r\n<p>\ub458\uc9f8 \uc904\uc5d0\ub294 inputSeq[0], ..., inputSeq[n-1]\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; inputSeq[i] &le; 1,000,000,000)<\/p>\r\n","output":"<p>countReplacement\ud568\uc218\uc758 \ub9ac\ud134\uac12\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<table class=\"table table-bordered\" style=\"width:50%\">\r\n\t<thead>\r\n\t\t<tr>\r\n\t\t\t<th>inputSeq<\/th>\r\n\t\t\t<th>\ub9ac\ud134 \uac12<\/th>\r\n\t\t\t<th>\uad50\uccb4 \uc218\uc5f4<\/th>\r\n\t\t<\/tr>\r\n\t<\/thead>\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td>(1, 2, 7, 6)<\/td>\r\n\t\t\t<td>2<\/td>\r\n\t\t\t<td>(3, 4, 5) or (4, 5, 3)<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>(2, 3, 4, 12, 6, 7, 1)<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>(5, 8, 9, 10, 11)<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>(4, 7, 4, 7)<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>inputSeq\uac00 \uace4\ub3cc\ub77c \uc218\uc5f4\uc774 \uc544\ub2d8<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>(3, 4)<\/td>\r\n\t\t\t<td>2<\/td>\r\n\t\t\t<td>(1, 2) or (2, 1)<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"10074","problem_lang":"1","title":"Gondola - Count Replacement Sequences","description":"<p>Mao-Kong Gondola is a famous attraction in Taipei. The gondola system consists of a circular rail, a single station, and n gondolas numbered consecutively from 1 to n running around the rail in a fixed direction. After gondola i passes the station, the next gondola to pass the station will be gondola i+1 if i &lt; n, or gondola 1 if i = n.<\/p>\r\n\r\n<p>Gondolas may break down. Luckily we have an infinite supply of spare gondolas, which are numbered n+1, n+2, and so on. When a gondola breaks down we replace it (in the same position on the track) with the first available spare gondola, that is, the one with the lowest number. For example, if there are five gondolas and gondola 1 breaks down, then we will replace it with gondola 6.<\/p>\r\n\r\n<p>You like to stand at the station and watch the gondolas as they pass by. A gondola sequence is a sequence of n numbers of gondolas that pass the station. It is possible that one or more gondolas broke down (and were replaced) before you arrived, but none of the gondolas break down while you are watching.<\/p>\r\n\r\n<p>Note that the same configuration of gondolas on the rail can give multiple gondola sequences, depending on which gondola passes first when you arrive at the station. For example, if none of the gondolas have broken down then both (2, 3, 4, 5, 1) and (4, 5, 1, 2, 3) are possible gondola sequences, but (4, 3, 2, 5, 1) is not (because the gondolas appear in the wrong order).<\/p>\r\n\r\n<p>If gondola 1 breaks down, then we might now observe the gondola sequence (4, 5, 6, 2, 3). If gondola 4 breaks down next, we replace it with gondola 7 and we might observe the gondola sequence (6, 2, 3, 7, 5). If gondola 7 breaks down after this, we replace it with gondola 8 and we may now observe the gondola sequence (3, 8, 5, 6, 2).<\/p>\r\n\r\n<table class=\"table table-bordered\" style=\"width:40%\">\r\n\t<thead>\r\n\t\t<tr>\r\n\t\t\t<th>broken gondola<\/th>\r\n\t\t\t<th>new gondola<\/th>\r\n\t\t\t<th>possible gondola sequence<\/th>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t<\/tr>\r\n\t<\/thead>\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>6<\/td>\r\n\t\t\t<td>(4, 5, 6, 2, 3)<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>4<\/td>\r\n\t\t\t<td>7<\/td>\r\n\t\t\t<td>(6, 2, 3, 7, 5)<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>7<\/td>\r\n\t\t\t<td>8<\/td>\r\n\t\t\t<td>(3, 8, 5, 6, 2)<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n\r\n<p>A replacement sequence is a sequence consisting of the numbers of the gondolas that have broken down, in the order in which they break down. In the previous example the replacement sequence is (1, 4, 7). A replacement sequence r produces a gondola sequence g if, after gondolas break down according to the replacement sequence r, the gondola sequence g may be observed.<\/p>\r\n\r\n<p>You must count the number of possible replacement sequences that produce a given sequence (which may or may not be a gondola sequence), modulo 1,000,000,009. You need to implement a function countReplacement.<\/p>\r\n\r\n<ul>\r\n\t<li>countReplacement(n, inputSeq)\r\n\t<ul>\r\n\t\t<li>n: the length of the input sequence.<\/li>\r\n\t\t<li>inputSeq: array of length ; inputSeq[i] is element of the input sequence, for 0 &le; i &le; n-1.<\/li>\r\n\t\t<li>If the input sequence is a gondola sequence, then count the number of replacement sequences that produce this gondola sequence (which could be extremely large), and return this number modulo 1,000,000,009. If the input sequence is not a gondola sequence, the function should return 0. If the input sequence is a gondola sequence but no gondolas broke down, the function should return 1.<\/li>\r\n\t<\/ul>\r\n\t<\/li>\r\n<\/ul>\r\n","input":"<p>line 1: n, the length of the input sequence.<\/p>\r\n\r\n<p>line 2: this line contains inputSeq[0], ..., inputSeq[n-1].<\/p>\r\n","output":"<p>Print return value of function countReplacement.<\/p>\r\n","hint":"<table class=\"table table-bordered\" style=\"width:411px\">\r\n\t<thead>\r\n\t\t<tr>\r\n\t\t\t<th>inputSeq<\/th>\r\n\t\t\t<th>return value<\/th>\r\n\t\t\t<th>replacement sequence<\/th>\r\n\t\t<\/tr>\r\n\t<\/thead>\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td>(1, 2, 7, 6)<\/td>\r\n\t\t\t<td>2<\/td>\r\n\t\t\t<td>(3, 4, 5) or (4, 5, 3)<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>(2, 3, 4, 12, 6, 7, 1)<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>(5, 8, 9, 10, 11)<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>(4, 7, 4, 7)<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>inputSeq is not a gondola sequence<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>(3, 4)<\/td>\r\n\t\t\t<td>2<\/td>\r\n\t\t\t<td>(1, 2) or (2, 1)<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]