시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 (하단 참고)512 MB37141242.857%

문제

Bob은 이분 그래프 (Bipartite Graph)를 이용한 놀이를 즐겨한다. 이 문제에서는 아래와 같이 임의의 이분 그래프 $H = (X + Y, E)$를 정의한다:

  • $n$개의 노드 집합 $X = \{x_1, x_2, \dots, x_n \}$ 과 $m$개의 노드 집합 $Y = \{ y_1, y_2, \dots, y_m\}$ 은 분리되어 있고, 따라서 $H$의 모든 간선은 $X$의 노드 중 하나와 $Y$의 노드 중 하나를 연결한다.
  • 간선 집합은 $E = \{ e_1, e_2, \dots, e_k \}$로 나타낸다.

Bob은 아래 규칙에 따라 이분 그래프 놀이를 한다:

  • $X$의 각 노드 $x_i$에 서로 다른 1부터 n 사이의 정수 가중치 $v_i$를 부여한다. (즉, $1 \leq i \leq n$ 인 $i$에 대하여 $1 \leq v_i \leq n$, $v_i \in \mathbb{Z}$ 이고 $i \neq j$ 일 때 $v_i \neq v_j$ 이다.)
  • $Y$의 각 노드 $y_j$에 서로 다른 1부터 m 사이의 정수 가중치 $w_j$를 부여한다 (즉, $1 \leq j \leq m$인 $j$에 대하여 $1 \leq w_j \leq m$, $w_j \in \mathbb{Z}$ 이고 $i \neq j$ 일 때 $w_i \neq w_j$ 이다.)
  • 위 가중치를 토대로 각 간선 $e = (x_i, y_j)$ 에 대해 간선의 가중치는 $v_i + w_j$ 로 정의한다.
  • 이분 그래프 H의 "점수"는 모든 간선의 가중치 합으로 정의한다.

예를 들어 X = {x1, x2}, Y = {y1, y2}, E = {(x1, y1), (x2, y1), (x2, y2)}라 하자 (아래 그림 참고).

이 때 위 규칙에 따라 노드들에 가중치를 부여하는 방법은 총 2! × 2! = 4가지 존재한다.

  • 만약 v1 = 1, v2 = 2이고 w1 = 1, w2 = 2라면: e1 = v1 + w1 = 2, e2 = v2 + w1 = 3, e3 = v2 + w2 = 4가 되어 H의 점수는 9가 된다.
  • 만약 v1 = 1, v2 = 2이고 w1 = 2, w2 = 1라면: e1 = v1 + w1 = 3, e2 = v2 + w1 = 4, e3 = v2 + w2 = 3가 되어 H의 점수는 10이 된다.
  • 만약 v1 = 2, v2 = 1이고 w1 = 1, w2 = 2라면: e1 = v1 + w1 = 3, e2 = v2 + w1 = 2, e3 = v2 + w2 = 3가 되어 H의 점수는 8이 된다.
  • 만약 v1 = 2, v2 = 1이고 w1 = 2, w2 = 1라면: e1 = v1 + w1 = 4, e2 = v2 + w1 = 3, e3 = v2 + w2 = 2가 되어 H의 점수는 9가 된다.

H의 "최대 점수"는 위와 같이 가능한 모든 가중치를 부여하는 방법 중 H의 점수를 최대화 했을 때 얻을 수 있는 점수로 정의하자 -- 편의상 이를 S(H)라 하자. Bob은 임의의 이분 그래프 H의 "최대 점수"를 구하는 놀이를 즐겨하지만 이제 너무 잘하게 되어 지루해하던 참이다.

마침 이를 지켜보던 Alice는 새로운 놀이를 제안했다. 그래프 H의 간선 중 임의로 i번째 간선을 지워 새로운 이분 그래프를 얻을 수 있는데, 이를 Hi라 하자 (아래 그림 참고).

S(Hi)는 그래프 Hi의 "최대 점수"이며 상기한 정의에 따라 구할 수 있다. 예를 들어 위의 예제에서 H1은 원래 그래프 H에서 (x1, y1)을 삭제한 그래프이며, 이 때 S(H1)은 7이다 (이를 달성하려면 v1 = 1, v2 = 2 이어야 한다). 같은 예제에서 H2은 (x2, y1)을 삭제한 그래프이며, 이 때 (v1, v2, w1, w2) 값에 관계없이 S(H2)는 6이다. S(H3)은 7이며, 따라서 이 경우 S(H1), S(H2), S(H3) 의 최댓값은 7이다.

Alice의 제안대로 Bob은 S(H)뿐 아니라 S(H1), S(H2), ..., S(Hk)의 최댓값을 구해보려고 한다. Bob을 도와주자.

입력

입력 첫 줄에 테스트 케이스의 수 T가 주어진다.

각 테스트 케이스의 첫 줄에는 n, m, k가 공백으로 구분되어 주어진다. 다음 k개의 줄에는 각 줄에 간선을 나타내는 2개의 정수가 공백으로 구분되어 주어지며 X의 노드 인덱스와 Y의 노드 인덱스를 나타낸다 (즉, xi와 yj를 잇는 간선은 "i j"로 주어진다).

출력

각 테스트 케이스의 정답인 두 개의 정수를 각 줄에 출력한다. 첫 번째 정수는 S(H)이며 두 번째 정수는 S(H1), ..., S(Hk)의 최댓값이다.

제한

  • 1 ≤ T ≤ 10
  • 1 ≤ n, m ≤ 10,000
  • 1 ≤ k ≤ 100,000

예제 입력 1

3
1 5 2
1 5
1 4
2 2 3
1 1
2 1
2 2
3 2 4
1 1
2 1
2 2
3 2

예제 출력 1

11 6
10 7
15 13

예제 1: 한 가지 방법으로 v1 = 1, w4 = 4, w5 = 5인 경우 S(H) = 11이 된다. S(H1) = S(H2) = 6이다.

예제 2: 본문에서 다루었다.

예제 3: 설명 없음.

[{"problem_id":"25575","problem_lang":"0","title":"\uc774\ubd84 \uadf8\ub798\ud504 \ub180\uc774","description":"<p>Bob\uc740 \uc774\ubd84 \uadf8\ub798\ud504 (Bipartite Graph)\ub97c \uc774\uc6a9\ud55c \ub180\uc774\ub97c \uc990\uaca8\ud55c\ub2e4. \uc774 \ubb38\uc81c\uc5d0\uc11c\ub294 \uc544\ub798\uc640 \uac19\uc774 \uc784\uc758\uc758 \uc774\ubd84 \uadf8\ub798\ud504 $H = (X + Y, E)$\ub97c \uc815\uc758\ud55c\ub2e4:<\/p>\r\n\r\n<ul>\r\n\t<li>$n$\uac1c\uc758 \ub178\ub4dc \uc9d1\ud569 $X = \\{x_1, x_2, \\dots, x_n \\}$ \uacfc $m$\uac1c\uc758 \ub178\ub4dc \uc9d1\ud569 $Y = \\{ y_1, y_2, \\dots, y_m\\}$ \uc740 \ubd84\ub9ac\ub418\uc5b4 \uc788\uace0, \ub530\ub77c\uc11c $H$\uc758 \ubaa8\ub4e0 \uac04\uc120\uc740 $X$\uc758 \ub178\ub4dc \uc911 \ud558\ub098\uc640 $Y$\uc758 \ub178\ub4dc \uc911 \ud558\ub098\ub97c \uc5f0\uacb0\ud55c\ub2e4.<\/li>\r\n\t<li>\uac04\uc120 \uc9d1\ud569\uc740 $E = \\{ e_1, e_2, \\dots, e_k \\}$\ub85c \ub098\ud0c0\ub0b8\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>Bob\uc740 \uc544\ub798 \uaddc\uce59\uc5d0 \ub530\ub77c \uc774\ubd84 \uadf8\ub798\ud504 \ub180\uc774\ub97c \ud55c\ub2e4:<\/p>\r\n\r\n<ul>\r\n\t<li>$X$\uc758 \uac01 \ub178\ub4dc $x_i$\uc5d0 \uc11c\ub85c \ub2e4\ub978 1\ubd80\ud130 n \uc0ac\uc774\uc758 \uc815\uc218 \uac00\uc911\uce58 $v_i$\ub97c \ubd80\uc5ec\ud55c\ub2e4. (\uc989, $1 \\leq i \\leq n$ \uc778 $i$\uc5d0 \ub300\ud558\uc5ec $1 \\leq v_i \\leq n$, $v_i \\in \\mathbb{Z}$ \uc774\uace0 $i \\neq j$ \uc77c \ub54c $v_i \\neq v_j$ \uc774\ub2e4.)<\/li>\r\n\t<li>$Y$\uc758 \uac01 \ub178\ub4dc $y_j$\uc5d0 \uc11c\ub85c \ub2e4\ub978 1\ubd80\ud130 m \uc0ac\uc774\uc758 \uc815\uc218 \uac00\uc911\uce58 $w_j$\ub97c \ubd80\uc5ec\ud55c\ub2e4 (\uc989, $1 \\leq j \\leq m$\uc778 $j$\uc5d0 \ub300\ud558\uc5ec $1 \\leq w_j \\leq m$, $w_j \\in \\mathbb{Z}$ \uc774\uace0 $i \\neq j$ \uc77c \ub54c $w_i \\neq w_j$ \uc774\ub2e4.)<\/li>\r\n\t<li>\uc704 \uac00\uc911\uce58\ub97c \ud1a0\ub300\ub85c \uac01 \uac04\uc120 $e = (x_i, y_j)$ \uc5d0 \ub300\ud574 \uac04\uc120\uc758 \uac00\uc911\uce58\ub294 $v_i + w_j$ \ub85c \uc815\uc758\ud55c\ub2e4.<\/li>\r\n\t<li>\uc774\ubd84 \uadf8\ub798\ud504 H\uc758 &quot;\uc810\uc218&quot;\ub294 \ubaa8\ub4e0 \uac04\uc120\uc758 \uac00\uc911\uce58 \ud569\uc73c\ub85c \uc815\uc758\ud55c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4 X = {x<sub>1<\/sub>, x<sub>2<\/sub>}, Y = {y<sub>1<\/sub>, y<sub>2<\/sub>}, E = {(x<sub>1<\/sub>, y<sub>1<\/sub>), (x<sub>2<\/sub>, y<sub>1<\/sub>), (x<sub>2<\/sub>, y<sub>2<\/sub>)}\ub77c \ud558\uc790 (\uc544\ub798 \uadf8\ub9bc \ucc38\uace0).<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/48591093-e5a3-4c92-ae62-90cd5a139c79\/-\/preview\/\" style=\"height: 250px; width: 290px;\" \/><\/p>\r\n\r\n<p>\uc774 \ub54c \uc704 \uaddc\uce59\uc5d0 \ub530\ub77c \ub178\ub4dc\ub4e4\uc5d0 \uac00\uc911\uce58\ub97c \ubd80\uc5ec\ud558\ub294 \ubc29\ubc95\uc740 \ucd1d 2! &times; 2! = 4\uac00\uc9c0 \uc874\uc7ac\ud55c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\ub9cc\uc57d v<sub>1<\/sub> = 1, v<sub>2<\/sub> = 2\uc774\uace0 w<sub>1<\/sub> = 1, w<sub>2<\/sub> = 2\ub77c\uba74: e<sub>1<\/sub> = v<sub>1<\/sub> + w<sub>1<\/sub> = 2, e<sub>2<\/sub> = v<sub>2<\/sub> + w<sub>1<\/sub> = 3, e<sub>3<\/sub> = v<sub>2<\/sub> + w<sub>2<\/sub> = 4\uac00 \ub418\uc5b4 H\uc758 \uc810\uc218\ub294 9\uac00 \ub41c\ub2e4.<\/li>\r\n\t<li>\ub9cc\uc57d v<sub>1<\/sub> = 1, v<sub>2<\/sub> = 2\uc774\uace0 w<sub>1<\/sub> = 2, w<sub>2<\/sub> = 1\ub77c\uba74: e<sub>1<\/sub> = v<sub>1<\/sub> + w<sub>1<\/sub> = 3, e<sub>2<\/sub> = v<sub>2<\/sub> + w<sub>1<\/sub> = 4, e<sub>3<\/sub> = v<sub>2<\/sub> + w<sub>2<\/sub> = 3\uac00 \ub418\uc5b4 H\uc758 \uc810\uc218\ub294 10\uc774 \ub41c\ub2e4.<\/li>\r\n\t<li>\ub9cc\uc57d v<sub>1<\/sub> = 2, v<sub>2<\/sub> = 1\uc774\uace0 w<sub>1<\/sub> = 1, w<sub>2<\/sub> = 2\ub77c\uba74: e<sub>1<\/sub> = v<sub>1<\/sub> + w<sub>1<\/sub> = 3, e<sub>2<\/sub> = v<sub>2<\/sub> + w<sub>1<\/sub> = 2, e<sub>3<\/sub> = v<sub>2<\/sub> + w<sub>2<\/sub> = 3\uac00 \ub418\uc5b4 H\uc758 \uc810\uc218\ub294 8\uc774 \ub41c\ub2e4.<\/li>\r\n\t<li>\ub9cc\uc57d v<sub>1<\/sub> = 2, v<sub>2<\/sub> = 1\uc774\uace0 w<sub>1<\/sub> = 2, w<sub>2<\/sub> = 1\ub77c\uba74: e<sub>1<\/sub> = v<sub>1<\/sub> + w<sub>1<\/sub> = 4, e<sub>2<\/sub> = v<sub>2<\/sub> + w<sub>1<\/sub> = 3, e<sub>3<\/sub> = v<sub>2<\/sub> + w<sub>2<\/sub> = 2\uac00 \ub418\uc5b4 H\uc758 \uc810\uc218\ub294 9\uac00 \ub41c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>H\uc758 &quot;\ucd5c\ub300 \uc810\uc218&quot;\ub294 \uc704\uc640 \uac19\uc774 \uac00\ub2a5\ud55c \ubaa8\ub4e0 \uac00\uc911\uce58\ub97c \ubd80\uc5ec\ud558\ub294 \ubc29\ubc95 \uc911 H\uc758 \uc810\uc218\ub97c \ucd5c\ub300\ud654 \ud588\uc744 \ub54c \uc5bb\uc744 \uc218 \uc788\ub294 \uc810\uc218\ub85c \uc815\uc758\ud558\uc790 -- \ud3b8\uc758\uc0c1 \uc774\ub97c S(H)\ub77c \ud558\uc790. Bob\uc740 \uc784\uc758\uc758 \uc774\ubd84 \uadf8\ub798\ud504 H\uc758 &quot;\ucd5c\ub300 \uc810\uc218&quot;\ub97c \uad6c\ud558\ub294 \ub180\uc774\ub97c \uc990\uaca8\ud558\uc9c0\ub9cc \uc774\uc81c \ub108\ubb34 \uc798\ud558\uac8c \ub418\uc5b4 \uc9c0\ub8e8\ud574\ud558\ub358 \ucc38\uc774\ub2e4.<\/p>\r\n\r\n<p>\ub9c8\uce68 \uc774\ub97c \uc9c0\ucf1c\ubcf4\ub358 Alice\ub294 \uc0c8\ub85c\uc6b4 \ub180\uc774\ub97c \uc81c\uc548\ud588\ub2e4. \uadf8\ub798\ud504 H\uc758 \uac04\uc120 \uc911 \uc784\uc758\ub85c i\ubc88\uc9f8 \uac04\uc120\uc744 \uc9c0\uc6cc \uc0c8\ub85c\uc6b4 \uc774\ubd84 \uadf8\ub798\ud504\ub97c \uc5bb\uc744 \uc218 \uc788\ub294\ub370, \uc774\ub97c H<sub>i<\/sub>\ub77c \ud558\uc790 (\uc544\ub798 \uadf8\ub9bc \ucc38\uace0).<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/85152b30-80e3-4984-ae32-5ee6a4287afd\/-\/preview\/\" style=\"height: 264px; width: 290px;\" \/><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/3ef6d24a-139f-4d5e-89db-1a5f962bed5b\/-\/preview\/\" style=\"height: 265px; width: 290px;\" \/><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/999d09b9-61b2-4afa-a6b0-f045eabba248\/-\/preview\/\" style=\"height: 266px; width: 290px;\" \/><\/p>\r\n\r\n<p>S(H<sub>i<\/sub>)\ub294 \uadf8\ub798\ud504 H<sub>i<\/sub>\uc758 &quot;\ucd5c\ub300 \uc810\uc218&quot;\uc774\uba70 \uc0c1\uae30\ud55c \uc815\uc758\uc5d0 \ub530\ub77c \uad6c\ud560 \uc218 \uc788\ub2e4. \uc608\ub97c \ub4e4\uc5b4 \uc704\uc758 \uc608\uc81c\uc5d0\uc11c H<sub>1<\/sub>\uc740 \uc6d0\ub798 \uadf8\ub798\ud504 H\uc5d0\uc11c (x<sub>1<\/sub>, y<sub>1<\/sub>)\uc744 \uc0ad\uc81c\ud55c \uadf8\ub798\ud504\uc774\uba70, \uc774 \ub54c S(H<sub>1<\/sub>)\uc740 7\uc774\ub2e4 (\uc774\ub97c \ub2ec\uc131\ud558\ub824\uba74 v<sub>1<\/sub> = 1, v<sub>2<\/sub> = 2 \uc774\uc5b4\uc57c \ud55c\ub2e4). \uac19\uc740 \uc608\uc81c\uc5d0\uc11c H<sub>2<\/sub>\uc740 (x<sub>2<\/sub>, y<sub>1<\/sub>)\uc744 \uc0ad\uc81c\ud55c \uadf8\ub798\ud504\uc774\uba70, \uc774 \ub54c (v<sub>1<\/sub>, v<sub>2<\/sub>, w<sub>1<\/sub>, w<sub>2<\/sub>) \uac12\uc5d0 \uad00\uacc4\uc5c6\uc774 S(H<sub>2<\/sub>)\ub294 6\uc774\ub2e4. S(H<sub>3<\/sub>)\uc740 7\uc774\uba70, \ub530\ub77c\uc11c \uc774 \uacbd\uc6b0 S(H<sub>1<\/sub>), S(H<sub>2<\/sub>), S(H<sub>3<\/sub>) \uc758 \ucd5c\ub313\uac12\uc740 7\uc774\ub2e4.<\/p>\r\n\r\n<p>Alice\uc758 \uc81c\uc548\ub300\ub85c Bob\uc740 S(H)\ubfd0 \uc544\ub2c8\ub77c S(H<sub>1<\/sub>), S(H<sub>2<\/sub>), ..., S(H<sub>k<\/sub>)\uc758 \ucd5c\ub313\uac12\uc744 \uad6c\ud574\ubcf4\ub824\uace0 \ud55c\ub2e4. Bob\uc744 \ub3c4\uc640\uc8fc\uc790.<\/p>\r\n","input":"<p>\uc785\ub825 \uccab \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uc218 T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab \uc904\uc5d0\ub294 n, m, k\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. \ub2e4\uc74c k\uac1c\uc758 \uc904\uc5d0\ub294 \uac01 \uc904\uc5d0 \uac04\uc120\uc744 \ub098\ud0c0\ub0b4\ub294 2\uac1c\uc758 \uc815\uc218\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c0\uba70 X\uc758 \ub178\ub4dc \uc778\ub371\uc2a4\uc640 Y\uc758 \ub178\ub4dc \uc778\ub371\uc2a4\ub97c \ub098\ud0c0\ub0b8\ub2e4 (\uc989, x<sub>i<\/sub>\uc640 y<sub>j<\/sub>\ub97c \uc787\ub294 \uac04\uc120\uc740 &quot;i j&quot;\ub85c \uc8fc\uc5b4\uc9c4\ub2e4).<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uc815\ub2f5\uc778 \ub450 \uac1c\uc758 \uc815\uc218\ub97c \uac01 \uc904\uc5d0 \ucd9c\ub825\ud55c\ub2e4. \uccab \ubc88\uc9f8 \uc815\uc218\ub294 S(H)\uc774\uba70 \ub450 \ubc88\uc9f8 \uc815\uc218\ub294 S(H<sub>1<\/sub>), ..., S(H<sub>k<\/sub>)\uc758 \ucd5c\ub313\uac12\uc774\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n\t<li>1 &le; T &le; 10<\/li>\r\n\t<li>1 &le; n, m &le; 10,000<\/li>\r\n\t<li>1 &le; k &le; 100,000<\/li>\r\n<\/ul>\r\n","sample_explain_1":"<p>\uc608\uc81c 1: \ud55c \uac00\uc9c0 \ubc29\ubc95\uc73c\ub85c v<sub>1<\/sub> = 1, w<sub>4<\/sub> = 4, w<sub>5<\/sub> = 5\uc778 \uacbd\uc6b0 S(H) = 11\uc774 \ub41c\ub2e4. S(H<sub>1<\/sub>) = S(H<sub>2<\/sub>) = 6\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc608\uc81c 2: \ubcf8\ubb38\uc5d0\uc11c \ub2e4\ub8e8\uc5c8\ub2e4.<\/p>\r\n\r\n<p>\uc608\uc81c 3: \uc124\uba85 \uc5c6\uc74c.<\/p>\r\n"},{"problem_id":"25575","problem_lang":"1","title":"Bipartite Graph Game","description":"<p>Bob likes to play a game using bipartite graphs. We define a bipartite graph $H = (X + Y, E)$ as follows:<\/p>\r\n\r\n<ul>\r\n\t<li>An n-node set $X = \\{ x_1, x_2, \\dots, x_n\\}$&nbsp;and an m-node set $Y = \\{ y_1, y_2, \\dots, y_m\\}$ are disjoint, and thus every edge in $H$ connects one node in $X$ with one node in $Y$.<\/li>\r\n\t<li>The edge set is represented by $E = \\{e_1, e_2, \\dots, e_k\\}$.<\/li>\r\n<\/ul>\r\n\r\n<p>Bob plays the bipartite graph game as follows:<\/p>\r\n\r\n<ul>\r\n\t<li>To&nbsp;each node $x_i$ in $X$, a distinct&nbsp;integer weight $v_i$&nbsp; between 1 and $n$ is assigned. That is,&nbsp;$1 \\leq v_i \\leq n$ &amp; $v_i \\in \\mathbb{Z}$&nbsp;for each $i$ with $1 \\leq i \\leq n$ and $v_i \\neq v_j$ when&nbsp;$i \\neq j$.<\/li>\r\n\t<li>To each node $y_j$ in $Y$, a distinct integer weight $w_j$ between 1 and $m$ is assigned. That is, $1 \\leq w_j \\leq m$ &amp; $w_j \\in \\mathbb{Z}$ for each $j$ with $1 \\leq j \\leq m$ and $w_i \\neq w_j$ when $i \\neq j$.<\/li>\r\n\t<li>Given this, the weight of an edge $e = (x_i, y_j)$ is defined as $v_i + w_j$.<\/li>\r\n\t<li>The &quot;<em>score&quot;<\/em>&nbsp;of $H$ is defined as the sum of the weights of all edges.<\/li>\r\n<\/ul>\r\n\r\n<p>For instance, suppose X = {x<sub>1<\/sub>, x<sub>2<\/sub>}, Y = {y<sub>1<\/sub>, y<sub>2<\/sub>}, and E = {(x<sub>1<\/sub>, y<sub>1<\/sub>), (x<sub>2<\/sub>, y<sub>1<\/sub>), (x<sub>2<\/sub>, y<sub>2<\/sub>)} as shown below.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/48591093-e5a3-4c92-ae62-90cd5a139c79\/-\/preview\/\" style=\"height: 250px; width: 290px;\" \/><\/p>\r\n\r\n<p>There are&nbsp;2! &times; 2! = 4 ways to assign weights to the nodes as above.<\/p>\r\n\r\n<ul>\r\n\t<li>If v<sub>1<\/sub> = 1, v<sub>2<\/sub> = 2 and&nbsp;w<sub>1<\/sub> = 1, w<sub>2<\/sub> = 2: e<sub>1<\/sub> = v<sub>1<\/sub> + w<sub>1<\/sub> = 2, e<sub>2<\/sub> = v<sub>2<\/sub> + w<sub>1<\/sub> = 3, e<sub>3<\/sub> = v<sub>2<\/sub> + w<sub>2<\/sub> = 4, and thus the score of H is 9.<\/li>\r\n\t<li>If v<sub>1<\/sub> = 1, v<sub>2<\/sub> = 2 and w<sub>1<\/sub> = 2, w<sub>2<\/sub> = 1: e<sub>1<\/sub> = v<sub>1<\/sub> + w<sub>1<\/sub> = 3, e<sub>2<\/sub> = v<sub>2<\/sub> + w<sub>1<\/sub> = 4, e<sub>3<\/sub> = v<sub>2<\/sub> + w<sub>2<\/sub> = 3, and thus the score of H is 10.<\/li>\r\n\t<li>If v<sub>1<\/sub> = 2, v<sub>2<\/sub> = 1 and w<sub>1<\/sub> = 1, w<sub>2<\/sub> = 2: e<sub>1<\/sub> = v<sub>1<\/sub> + w<sub>1<\/sub> = 3, e<sub>2<\/sub> = v<sub>2<\/sub> + w<sub>1<\/sub> = 2, e<sub>3<\/sub> = v<sub>2<\/sub> + w<sub>2<\/sub> = 3, and thus the score of H is 8.<\/li>\r\n\t<li>If v<sub>1<\/sub> = 2, v<sub>2<\/sub> = 1 and w<sub>1<\/sub> = 2, w<sub>2<\/sub> = 1: e<sub>1<\/sub> = v<sub>1<\/sub> + w<sub>1<\/sub> = 4, e<sub>2<\/sub> = v<sub>2<\/sub> + w<sub>1<\/sub> = 3, e<sub>3<\/sub> = v<sub>2<\/sub> + w<sub>2<\/sub> = 2, and thus the score of H is 9.<\/li>\r\n<\/ul>\r\n\r\n<p>Let S(H) be the largest score of H we can obtain by assigning the weights. Bob is getting bored from&nbsp;computing S(H) as he is too good at it.<\/p>\r\n\r\n<p>Alice, noticing this, proposed a new game. Let H<sub>i<\/sub> be the graph you obtain by removing the i-th edge from H (see below).<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/85152b30-80e3-4984-ae32-5ee6a4287afd\/-\/preview\/\" style=\"height: 264px; width: 290px;\" \/><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/3ef6d24a-139f-4d5e-89db-1a5f962bed5b\/-\/preview\/\" style=\"height: 265px; width: 290px;\" \/><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/999d09b9-61b2-4afa-a6b0-f045eabba248\/-\/preview\/\" style=\"height: 266px; width: 290px;\" \/><\/p>\r\n\r\n<p>S(H<sub>i<\/sub>) is then the highest score achievable for H<sub>i<\/sub>, analogously. In the example above,&nbsp;H<sub>1&nbsp;<\/sub>is obtained by removing (x<sub>1<\/sub>, y<sub>1<\/sub>) in H, and S(H<sub>1<\/sub>) =&nbsp;7 (to achieve this, Bob should&nbsp;assign v<sub>1<\/sub> = 1, v<sub>2<\/sub> = 2). In the same example,&nbsp;H<sub>2&nbsp;<\/sub>is obtained by removing (x<sub>2<\/sub>, y<sub>1<\/sub>) in H, and S(H<sub>2<\/sub>) = 6 regardless of the weights (v<sub>1<\/sub>, v<sub>2<\/sub>, w<sub>1<\/sub>, w<sub>2<\/sub>). Lastly,&nbsp;S(H<sub>3<\/sub>) = 7, and thus the maximum of S(H<sub>1<\/sub>), S(H<sub>2<\/sub>), S(H<sub>3<\/sub>) is 7.<\/p>\r\n\r\n<p>Per Alice&#39;s suggestion, Bob wants to compute S(H) as well as the maximum of&nbsp;S(H<sub>1<\/sub>), S(H<sub>2<\/sub>), ..., S(H<sub>k<\/sub>). Let&#39;s help Bob.<\/p>\r\n","input":"<p>The first line of the input will contain T, the number of test cases.<\/p>\r\n\r\n<p>The first line of each test case will contain n, m, k, separated by whitespace. The next k lines will contain two integers (a node in X and a node in Y) in each line, describing an edge. If an edge connects x<sub>i<\/sub> and y<sub>j<\/sub>, then the input will be given as &quot;i j&quot;.<\/p>\r\n","output":"<p>Output each test case&#39;s answer (two integers) in each line. The first integer must be S(H) and the second the maximum of S(H<sub>1<\/sub>), ..., S(H<sub>k<\/sub>).<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","limit":"<ul>\r\n\t<li>1 &le; T &le; 10<\/li>\r\n\t<li>1 &le; n, m &le; 10,000<\/li>\r\n\t<li>1 &le; k &le; 100,000&nbsp;<\/li>\r\n<\/ul>\r\n","sample_explain_1":"<p>Case 1: One way is to assign v<sub>1<\/sub> = 1, w<sub>4<\/sub> = 4, w<sub>5<\/sub> = 5 to obtain S(H) = 11. S(H<sub>1<\/sub>) = S(H<sub>2<\/sub>) = 6 in this example.<\/p>\r\n\r\n<p>Case 2: Discussed in the problem statement.<\/p>\r\n\r\n<p>Case 3: No explanation.<\/p>\r\n"}]

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