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문제

N(1≤N≤100)개의 도시들로 이루어진 나라가 있다. 이들 중 몇 개의 도시들은 서로 도로로 연결되어 있다. 당신은 당신의 취미 생활인 자동차 드라이브를 즐기려고 한다. 각각의 도시는 0, 1, 2, …, N-1의 번호가 붙어 있고, 현재 당신은 S번 도시에 위치하고 있으며, 당신은 T번 도시로 이동하려 한다.

각각의 도로는 그 도로의 길이와, 그 도로를 이용할 때 생기는 피로도가 있다. 피로도 값은 때로는 음수일 수도 있는데, 이는 그 도로를 드라이브 할 때 만족감을 얻는 경우이다. 또한 같은 도시들을 연결하는 도로라 하더라도, 어느 방향으로 운전하느냐에 따라 마주치는 경치가 다르기 때문에 피로도 역시 달라질 수 있다.

당신은 가능하면 피로도 값의 총 합을 최소로 하는 경로로 이동하려 한다. 그런 경우가 여러 가지 있다면 길이의 총 합이 최소인 경로를 찾으려고 한다. 단, 당신은 이동을 할 때, 각각의 도시에 연결된 도로들 중 피로도가 최소인 도로만을 이용할 수 있다.

예를 들어 위와 같은 경우를 보자. 각 도로 위에 []로 둘러싸인 값이 그 도로의 길이이고, 좌우의 값은 각 방향으로 그 도로를 이용할 때의 피로도이다. 위의 예에서의  최적해는 0-2-4-3-5가 된다. 이 때의 피로도 합은 2(=-1+3+0+0)이고, 길이는 50(5+10+5+30)이다. 0-1-4-3-5 역시 피로도 합이 2이지만, 이는 길이가 51이기 때문에 최적해는 아니다. 0-3-5와 같은 경로는 피로도 합이 0이지만, 각 도시에 연결된 도로들 중 피로도가 최소인 도로만 이용한다는 조건에 어긋나므로 답이 될 수 없다.

각 도로들에 대한 정보를 입력받아 최적해를 구하는 프로그램을 작성하시오.

입력

첫째 줄에 네 정수 N, M(0≤M≤5,000), S, T가 주어진다. 다음 M개의 줄에는 각 도로에 대한 정보를 나타내는 다섯 정수 u, v, a, c, b 가 주어진다. 이는 u번 도시와 v번 도시를 연결하는 길이 c의 도로가 있고, u->v 방향으로는 피로도가 a, v->u 방향으로는 피로도가 b라는 의미이다. 길이는 1이상 100이하의 정수이고, 피로도는 -100이상 100이하의 정수이다. 두 도시 사이에 여러 개의 도로가 있을 수도 있다.

출력

첫째 줄에 피로도 총 합과 길이 총 합을 출력한다. 만약 최적해가 없다면 VOID를 출력한다. 만약 답이 무한히 작아질 수 있다면 UNBOUND를 출력한다.

예제 입력 1

7 11 0 5
0 1 -1 6 4
0 2 -1 5 4
0 3 0 1 0
1 4 3 10 1
2 4 3 10 1
3 4 0 5 0
3 5 0 30 0
3 5 1 20 0
4 6 0 3 1
6 5 1 8 0
6 6 0 2 -1

예제 출력 1

2 50

힌트

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\ucd5c\uc801\ud574\ub294 0-2-4-3-5\uac00 \ub41c\ub2e4. \uc774 \ub54c\uc758 \ud53c\ub85c\ub3c4 \ud569\uc740 2(=-1+3+0+0)\uc774\uace0, \uae38\uc774\ub294 50(5+10+5+30)\uc774\ub2e4. 0-1-4-3-5 \uc5ed\uc2dc \ud53c\ub85c\ub3c4 \ud569\uc774 2\uc774\uc9c0\ub9cc, \uc774\ub294 \uae38\uc774\uac00 51\uc774\uae30 \ub54c\ubb38\uc5d0 \ucd5c\uc801\ud574\ub294 \uc544\ub2c8\ub2e4. 0-3-5\uc640 \uac19\uc740 \uacbd\ub85c\ub294 \ud53c\ub85c\ub3c4 \ud569\uc774 0\uc774\uc9c0\ub9cc, \uac01 \ub3c4\uc2dc\uc5d0 \uc5f0\uacb0\ub41c \ub3c4\ub85c\ub4e4 \uc911 \ud53c\ub85c\ub3c4\uac00 \ucd5c\uc18c\uc778 \ub3c4\ub85c\ub9cc \uc774\uc6a9\ud55c\ub2e4\ub294 \uc870\uac74\uc5d0 \uc5b4\uae0b\ub098\ubbc0\ub85c \ub2f5\uc774 \ub420 \uc218 \uc5c6\ub2e4.<\/p>\r\n<p>\uac01 \ub3c4\ub85c\ub4e4\uc5d0 \ub300\ud55c \uc815\ubcf4\ub97c \uc785\ub825\ubc1b\uc544 \ucd5c\uc801\ud574\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ub124 \uc815\uc218 N, M(0&le;M&le;5,000), S, T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ub2e4\uc74c M\uac1c\uc758 \uc904\uc5d0\ub294 \uac01 \ub3c4\ub85c\uc5d0 \ub300\ud55c \uc815\ubcf4\ub97c \ub098\ud0c0\ub0b4\ub294 \ub2e4\uc12f \uc815\uc218 u, v, a, c, b \uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774\ub294 u\ubc88 \ub3c4\uc2dc\uc640 v\ubc88 \ub3c4\uc2dc\ub97c \uc5f0\uacb0\ud558\ub294 \uae38\uc774 c\uc758 \ub3c4\ub85c\uac00 \uc788\uace0, u-&gt;v \ubc29\ud5a5\uc73c\ub85c\ub294 \ud53c\ub85c\ub3c4\uac00 a, v-&gt;u \ubc29\ud5a5\uc73c\ub85c\ub294 \ud53c\ub85c\ub3c4\uac00 b\ub77c\ub294 \uc758\ubbf8\uc774\ub2e4. \uae38\uc774\ub294 1\uc774\uc0c1 100\uc774\ud558\uc758 \uc815\uc218\uc774\uace0, \ud53c\ub85c\ub3c4\ub294 -100\uc774\uc0c1 100\uc774\ud558\uc758 \uc815\uc218\uc774\ub2e4. \ub450 \ub3c4\uc2dc \uc0ac\uc774\uc5d0 \uc5ec\ub7ec \uac1c\uc758 \ub3c4\ub85c\uac00 \uc788\uc744 \uc218\ub3c4 \uc788\ub2e4.<\/p>","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \ud53c\ub85c\ub3c4 \ucd1d \ud569\uacfc \uae38\uc774 \ucd1d \ud569\uc744 \ucd9c\ub825\ud55c\ub2e4. \ub9cc\uc57d \ucd5c\uc801\ud574\uac00 \uc5c6\ub2e4\uba74 VOID\ub97c \ucd9c\ub825\ud55c\ub2e4. \ub9cc\uc57d \ub2f5\uc774 \ubb34\ud55c\ud788 \uc791\uc544\uc9c8 \uc218 \uc788\ub2e4\uba74 UNBOUND\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"2129","problem_lang":"1","title":"Adventurous Driving","description":"<p>After a period of intensive development of the transportation infrastructure, the government of Ruritania decides to take firm steps to strengthen citizens&#39; confidence in the national road network and sets up a compensation scheme for adventurous driving (CSAD). Those driving on a road with holes, bumps and other entertaining obstacles get compensation; those driving on a decent road pay tax. These compensations and taxes are obtained and paid in cash on entry on each road and depend on the entry point on the road. What you get and pay driving on a road from A to B may be different from what you get and pay driving on the same road from B to A. The Ruritarian authorities call fee the amount of money paid as tax or obtained as compensation on entry on a road. A positive fee is a tax; a negative fee stands for compensation.&nbsp;<\/p>\r\n\r\n<p>John Doe plans to take advantage of CSAD for saving money he needs to repair his old car. When driving from A to B, John follows a path he calls optimal: a path that is rewarding and has the minimal length out of the paths with the minimal weight from A to B. In John&#39;s opinion, a path is rewarding if all the roads in the path are rewarding, and a road (X,Y) is rewarding if it has the minimal entry fee out of the roads leaving X. The weight of a path is the sum of the entry fees paid along the path. The length of a path cumulates the length of the roads in the path. The problem is helping John to compute the weight and the length of an optimal path from A to B on a given map.&nbsp;<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/adriving.png\" style=\"float:right; height:122px; width:336px\" \/>For example, on the illustrated road map vertices designate cities and edges stand for roads. The label fuv[L]fvu of the road (u,v) shows the fee fuv for driving from u to v, the fee fvu for driving from v to u, and the length L of the road. The path (0,2,4,3,5) from 0 to 5 is optimal: it is rewarding, has weight 2 (-1+3+0+0) and length 50 (5+10+5+30). The path (0,1,4,3,5), although rewarding and of weight 2, has length 51. The path (0,3,5) has weight 0 and length 20 but it is not rewarding.&nbsp;<\/p>\r\n","input":"<p>Write a program that reads several data sets from a text file. Each data set encodes a road map and starts with four integers: the number 1&le;n&le;100 of towns on the map, the number 0&le;m&le;5000 of roads, the departure town 0&le;A&le;n-1, and the destination town 0&le;B&le;n-1. Follow m data quintuples (u,v,fuv[L]fvu), where u and v are town identifiers (integers in the range 0..n-1), 100&le;fuv, fvu&le;100 are integer fees for driving on the road (u,v), and 1&le;L&le;100 is the integer length of the road. The quintuples may occur in any order. Except the quintuples, which do not contain white spaces, white spaces may occur freely in input. Input data terminate with an end of file and are correct.<\/p>\r\n","output":"<p>For each data set, the program prints &ndash; from the beginning of a line &ndash; the weight and the length of an optimal path, according to John&#39;s oppinion, from A to B. If there is no optimal path from A to B the text VOID is printed. If the weight of the optimal path from A to B has no lower bound the text UNBOUND is printed.&nbsp;<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]