시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

방향성 있는 그래프 G가 주어진다. 모든 간선의 길이는 1일 때, 당신은 두 가지 쿼리를 처리해야 한다.

  1. 간선 하나를 제거한다.
  2. 정점 1에서 정점 i 까지의 최단 경로를 출력한다. 경로가 없으면 -1을 출력한다.

입력

첫 번째 줄에 그래프의 정점, 간선의 수와 질의의 수를 나타내는 n, m, q 가 주어진다. (1 ≤ n ≤ 1, 000, 1 ≤ m ≤ 100, 000, 1 ≤ q ≤ 200, 000) 정점들은 순서대로 1부터 n까지 번호가 매겨져 있고, 간선들은 순서대로 1부터 m까지 번호가 매겨져 있다.

이후 m개의 줄로 간선의 정보가 주어진다. i 번째 줄은 간선 i를 나타내며, 두 정수 u, v (1 ≤ u, v ≤ n, u ≠ v) 로 주어진다. 정점 u에서 정점 v로 가는 간선을 의미한다.

이후 q개의 줄에 질의가 순서대로 주어진다. 각각의 질의는 문자 t 와 정수 p 로 주어진다. (t ∈ {U, E})

만약 t = U 일 경우, p 번 간선이 제거된다. 이미 제거된 간선이 다시 제거되는 일은 없다. (1 ≤ p ≤ m)

만약 t = E 일 경우, 1번 정점에서 p번 정점으로 가는 최단 경로의 길이를 출력한다. 간선 하나당 길이가 1이라고 가정한다. 만약 경로가 없으면 -1을 출력한다. (2 ≤ p ≤ n) t = E 인 쿼리가 적어도 1개 있음이 보장된다.

출력

t = E인 질의 마다 1번 정점에서 p번 정점으로 가는 최단 경로의 길이를 한 줄씩 출력한다. 간선 하나당 길이가 1이라고 가정한다. 만약 경로가 없으면 -1을 출력한다. 질의가 주어진 순서대로 출력하라.

예제 입력 1

7 8 8
1 2
1 3
1 5
2 4
3 1
3 5
4 5
4 6
E 7
E 5
U 7
E 6
E 5
U 2
E 5
E 4

예제 출력 1

-1
1
3
1
1
2
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(1 &le; n &le; 1, 000, 1 &le; m &le; 100, 000, 1 &le; q &le; 200, 000) \uc815\uc810\ub4e4\uc740 \uc21c\uc11c\ub300\ub85c 1\ubd80\ud130 n\uae4c\uc9c0 \ubc88\ud638\uac00 \ub9e4\uaca8\uc838 \uc788\uace0, \uac04\uc120\ub4e4\uc740 \uc21c\uc11c\ub300\ub85c 1\ubd80\ud130 m\uae4c\uc9c0 \ubc88\ud638\uac00 \ub9e4\uaca8\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc774\ud6c4 m\uac1c\uc758 \uc904\ub85c \uac04\uc120\uc758 \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. i \ubc88\uc9f8 \uc904\uc740 \uac04\uc120 i\ub97c \ub098\ud0c0\ub0b4\uba70, \ub450 \uc815\uc218 u, v (1 &le; u, v &le; n, u &ne;&nbsp;v) \ub85c \uc8fc\uc5b4\uc9c4\ub2e4. \uc815\uc810 u\uc5d0\uc11c \uc815\uc810 v\ub85c \uac00\ub294 \uac04\uc120\uc744 \uc758\ubbf8\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc774\ud6c4 q\uac1c\uc758 \uc904\uc5d0 \uc9c8\uc758\uac00 \uc21c\uc11c\ub300\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. \uac01\uac01\uc758 \uc9c8\uc758\ub294 \ubb38\uc790 t \uc640 \uc815\uc218 p \ub85c \uc8fc\uc5b4\uc9c4\ub2e4. (t &isin; {U, E})<\/p>\r\n\r\n<p>\ub9cc\uc57d t = U \uc77c \uacbd\uc6b0, p \ubc88 \uac04\uc120\uc774 \uc81c\uac70\ub41c\ub2e4. \uc774\ubbf8 \uc81c\uac70\ub41c \uac04\uc120\uc774 \ub2e4\uc2dc \uc81c\uac70\ub418\ub294 \uc77c\uc740 \uc5c6\ub2e4. (1 &le; p &le; m)<\/p>\r\n\r\n<p>\ub9cc\uc57d t = E \uc77c \uacbd\uc6b0, 1\ubc88 \uc815\uc810\uc5d0\uc11c p\ubc88 \uc815\uc810\uc73c\ub85c \uac00\ub294 \ucd5c\ub2e8 \uacbd\ub85c\uc758 \uae38\uc774\ub97c \ucd9c\ub825\ud55c\ub2e4. \uac04\uc120 \ud558\ub098\ub2f9 \uae38\uc774\uac00 1\uc774\ub77c\uace0 \uac00\uc815\ud55c\ub2e4. \ub9cc\uc57d \uacbd\ub85c\uac00 \uc5c6\uc73c\uba74 -1\uc744 \ucd9c\ub825\ud55c\ub2e4. (2 &le; p &le; n) t = E \uc778 \ucffc\ub9ac\uac00 \uc801\uc5b4\ub3c4 1\uac1c \uc788\uc74c\uc774 \ubcf4\uc7a5\ub41c\ub2e4.<\/p>\r\n","output":"<p>t = E\uc778 \uc9c8\uc758 \ub9c8\ub2e4 1\ubc88 \uc815\uc810\uc5d0\uc11c p\ubc88 \uc815\uc810\uc73c\ub85c \uac00\ub294 \ucd5c\ub2e8 \uacbd\ub85c\uc758 \uae38\uc774\ub97c \ud55c \uc904\uc529 \ucd9c\ub825\ud55c\ub2e4. \uac04\uc120 \ud558\ub098\ub2f9 \uae38\uc774\uac00 1\uc774\ub77c\uace0 \uac00\uc815\ud55c\ub2e4. \ub9cc\uc57d \uacbd\ub85c\uac00 \uc5c6\uc73c\uba74 -1\uc744 \ucd9c\ub825\ud55c\ub2e4. \uc9c8\uc758\uac00 \uc8fc\uc5b4\uc9c4 \uc21c\uc11c\ub300\ub85c \ucd9c\ub825\ud558\ub77c.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"8452","problem_lang":"3","title":"Ewakuacja","description":"<p>Bajtocka Republika Bitowa organizuje przysz\u0142oroczne fina\u0142y Mistrzostw \u015awiata w Pi\u0142ce Bitowej. W przygotowaniach bierze udzia\u0142 Bajtazar, kt&oacute;ry odpowiada za opracowanie planu ewakuacji ze stadionu w ka\u017cdym mie\u015bcie, w kt&oacute;rym rozgrywane b\u0119d\u0105 mecze. Najwi\u0119cej problem&oacute;w sprawia mu plan ewakuacji dla Bajtogrodu, bo co rusz dostaje informacje o ulicach, kt&oacute;re b\u0119d\u0105 zamkni\u0119te w trakcie trwania fina\u0142&oacute;w, i musi poprawia\u0107 wcze\u015bniejsze ustalenia. Co jaki\u015b czas dostaje pytania od dzia\u0142aczy z Bajtockiego Zwi\u0105zku Pi\u0142ki Bitowej. Chc\u0105 oni wiedzie\u0107 jak szybko mo\u017cna si\u0119 ewakuowa\u0107 ze stadionu do wskazanego skrzy\u017cowania w mie\u015bcie.<\/p>\r\n\r\n<p>W Bajtogrodzie jest <em>n<\/em>&nbsp;skrzy\u017cowa\u0144 po\u0142\u0105czonych jednokierunkowymi ulicami. Ewakuacja musi przebiega\u0107 zgodnie z kierunkiem ulic. Przebycie ka\u017cdej ulicy \u0142\u0105cz\u0105cej dwa skrzy\u017cowania zajmuje dok\u0142adnie jedn\u0105 minut\u0119.<\/p>\r\n\r\n<p>Napisz program, kt&oacute;ry pomo\u017ce Bajtazarowi w pracy. Dla podanych informacji o zamkni\u0119ciach ulic powinien on oblicza\u0107 odpowiedzi na pytania dzia\u0142aczy.<\/p>\r\n","input":"<p>W pierwszym wierszu wej\u015bcia znajduj\u0105 si\u0119 trzy liczby ca\u0142kowite <em>n<\/em>, <em>m<\/em>&nbsp;i <em>q<\/em>&nbsp;(1 &le; <em>n<\/em> &le; 1 000, 1 &le; <em>m<\/em> &le; 100 000, 1 &le; <em>q<\/em> &le; 200 000) oznaczaj\u0105ce kolejno liczb\u0119 skrzy\u017cowa\u0144 w Bajtogrodzie, liczb\u0119 \u0142\u0105cz\u0105cych je ulic oraz liczb\u0119 zapyta\u0144. Skrzy\u017cowania s\u0105 ponumerowane liczbami od 1&nbsp;do <em>n<\/em>. Stadion znajduje si\u0119 przy skrzy\u017cowaniu numer 1. Ka\u017cdy z kolejnych <em>m<\/em>&nbsp;wierszy zawiera opis jednej ulicy w postaci dw&oacute;ch liczb ca\u0142kowitych <em>a<sub>i<\/sub><\/em>,&nbsp;<em>b<sub>i<\/sub><\/em>&nbsp;(1 &le; <em>a<sub>i<\/sub><\/em>, <em>b<sub>i<\/sub><\/em> &le; <em>n<\/em>, <em>a<sub>i<\/sub><\/em> &ne; <em>b<sub>i<\/sub><\/em>), kt&oacute;re oznaczaj\u0105, \u017ce z&nbsp;<em>a<sub>i<\/sub><\/em>&nbsp;do&nbsp;<em>b<sub>i<\/sub><\/em>&nbsp;prowadzi jednokierunkowa ulica, kt&oacute;rej przebycie zajmuje jedn\u0105 minut\u0119. Pomi\u0119dzy par\u0105 skrzy\u017cowa\u0144 b\u0119dzie co najwy\u017cej jedna ulica w ka\u017cdym kierunku.<\/p>\r\n\r\n<p>W kolejnych <em>q<\/em>&nbsp;wierszach znajduj\u0105 si\u0119 opisy zapyta\u0144 w kolejno\u015bci chronologicznej. Opis jednego zapytania sk\u0142ada si\u0119 ze znaku <em>t<sub>i<\/sub><\/em>&nbsp;(<em>t<sub>i<\/sub><\/em> &isin; {U, E}) oraz liczby ca\u0142kowitej&nbsp;<em>p<sub>i<\/sub><\/em>.<\/p>\r\n\r\n<p>Zapytanie rozpoczynaj\u0105ce si\u0119 od <em>t<sub>i<\/sub><\/em> = U&nbsp;opisuje informacj\u0119 o zamkni\u0119ciu ulicy. Liczba <em>p<sub>i<\/sub><\/em>&nbsp;zawiera si\u0119 w&oacute;wczas w przedziale [1,<em>m<\/em>]&nbsp;i oznacza numer zamkni\u0119tej ulicy. Ulice numerujemy zgodnie z kolejno\u015bci\u0105 na wej\u015bciu.<\/p>\r\n\r\n<p>Zapytanie rozpoczynaj\u0105ce si\u0119 od&nbsp;<em>t<sub>i<\/sub><\/em> = E&nbsp;oznacza pytanie o mo\u017cliwo\u015b\u0107 ewakuacji do skrzy\u017cowania numer <em>p<sub>i<\/sub><\/em>&nbsp;(w tym przypadku 2 &le; <em>p<sub>i<\/sub><\/em> &le; <em>n<\/em>). 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