시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 128 MB 859 89 54 17.143%

문제

상근이는 데이트 비용을 마련하기 위해 빠름택배에서 택배를 배달하는 직업을 가졌다.

매일 빠름택배에 출근하면, 상근이는 그날 배달해야 하는 위치가 적힌 종이를 받는다. 또, 이 위치에 적혀져있는 순서대로 배달해야 한다.

도시는 R*C칸으로 나누어져 있다. 각 행은 1번부터 R번까지 번호가 매겨져 있고, 열도 1번부터 C번까지 번호가 매겨져 있다.

상근이는 각 칸에서, 왼쪽 또는 오른쪽으로 이동할 수 있다. 하지만, 위나 아래로 이동하려면 꼭 첫 번째나 마지막 열(1과 C)로 가야 한다.

빠름택배는 가장 왼쪽 위 칸인 (1,1)에 있다. 이곳이 상근이가 배달을 시작하는 곳이다. 상근이는 출발할 때 모든 물품을 들고 출발하고, 자신의 오토바이를 이용하여 배달하기 때문에, 배달하는 중 또는 배달을 마치고 다시 빠름택배로 돌아오지 않는다.

각 칸을 통과하는데 드는 시간이 주어진다. 이때, 모든 택배를 배달하는데 걸리는 최소 시간을 계산하는 프로그램을 작성하시오.

입력

첫째 줄에 도시의 크기 R과 C가 주어진다. (1 ≤ R ≤ 2000, 1 ≤ C ≤ 200)

다음 R개 줄에는, 각 칸을 통과하는데 드는 시간이 주어진다. 이 시간은 0보다 크거나 같고, 5000보다 작거나 같은 자연수이다.

다음 줄에는 배달해야 하는 물품의 수 D (1 ≤ D ≤ 200000)가 주어진다. 다음 D개 줄에는 물품을 배달해야 하는 곳의 위치의 좌표가 배달해야 하는 순서대로 주어진다. 같은 곳이 여러 번 주어질 수는 있다. 하지만, 연속해서 같은 곳을 배달해야 하는 경우는 없다. 

출력

모든 택배를 배달하는데 가장 빠른 시간을 출력한다.

예제 입력 1

3 3
1 8 2
2 3 2
1 0 1
3
1 3
3 3
2 2

예제 출력 1

17

힌트

예제의 경우에는 아래와 같이 이동하면 된다.

(1, 1), (2, 1), (3, 1), (3, 2), (3, 3), (2, 3), (1, 3), (2, 3), (3, 3), (2, 3), (2, 2)

총 배달 시간은 1+2+1+0+1+2+2+2+1+2+3=17가 된다.

[{"problem_id":"2939","problem_lang":"0","title":"\ud0dd\ubc30 \ubc30\ub2ec","description":"<p>\uc0c1\uadfc\uc774\ub294 \ub370\uc774\ud2b8 \ube44\uc6a9\uc744 \ub9c8\ub828\ud558\uae30 \uc704\ud574 \ube60\ub984\ud0dd\ubc30\uc5d0\uc11c \ud0dd\ubc30\ub97c \ubc30\ub2ec\ud558\ub294 \uc9c1\uc5c5\uc744 \uac00\uc84c\ub2e4.<\/p>\r\n\r\n<p>\ub9e4\uc77c \ube60\ub984\ud0dd\ubc30\uc5d0 \ucd9c\uadfc\ud558\uba74, \uc0c1\uadfc\uc774\ub294 \uadf8\ub0a0 \ubc30\ub2ec\ud574\uc57c \ud558\ub294 \uc704\uce58\uac00 \uc801\ud78c \uc885\uc774\ub97c \ubc1b\ub294\ub2e4. \ub610, \uc774 \uc704\uce58\uc5d0 \uc801\ud600\uc838\uc788\ub294 \uc21c\uc11c\ub300\ub85c \ubc30\ub2ec\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub3c4\uc2dc\ub294 R*C\uce78\uc73c\ub85c \ub098\ub204\uc5b4\uc838 \uc788\ub2e4. \uac01 \ud589\uc740 1\ubc88\ubd80\ud130 R\ubc88\uae4c\uc9c0 \ubc88\ud638\uac00 \ub9e4\uaca8\uc838 \uc788\uace0, \uc5f4\ub3c4 1\ubc88\ubd80\ud130 C\ubc88\uae4c\uc9c0 \ubc88\ud638\uac00 \ub9e4\uaca8\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc0c1\uadfc\uc774\ub294 \uac01 \uce78\uc5d0\uc11c, \uc67c\ucabd \ub610\ub294 \uc624\ub978\ucabd\uc73c\ub85c \uc774\ub3d9\ud560 \uc218 \uc788\ub2e4. \ud558\uc9c0\ub9cc, \uc704\ub098 \uc544\ub798\ub85c \uc774\ub3d9\ud558\ub824\uba74 \uaf2d \uccab \ubc88\uc9f8\ub098 \ub9c8\uc9c0\ub9c9 \uc5f4(1\uacfc C)\ub85c \uac00\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ube60\ub984\ud0dd\ubc30\ub294 \uac00\uc7a5 \uc67c\ucabd \uc704 \uce78\uc778 (1,1)\uc5d0 \uc788\ub2e4. \uc774\uacf3\uc774 \uc0c1\uadfc\uc774\uac00 \ubc30\ub2ec\uc744 \uc2dc\uc791\ud558\ub294 \uacf3\uc774\ub2e4. \uc0c1\uadfc\uc774\ub294 \ucd9c\ubc1c\ud560 \ub54c \ubaa8\ub4e0 \ubb3c\ud488\uc744 \ub4e4\uace0 \ucd9c\ubc1c\ud558\uace0, \uc790\uc2e0\uc758 \uc624\ud1a0\ubc14\uc774\ub97c \uc774\uc6a9\ud558\uc5ec \ubc30\ub2ec\ud558\uae30 \ub54c\ubb38\uc5d0, \ubc30\ub2ec\ud558\ub294 \uc911 \ub610\ub294 \ubc30\ub2ec\uc744 \ub9c8\uce58\uace0 \ub2e4\uc2dc \ube60\ub984\ud0dd\ubc30\ub85c \ub3cc\uc544\uc624\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n\r\n<p>\uac01 \uce78\uc744 \ud1b5\uacfc\ud558\ub294\ub370 \ub4dc\ub294 \uc2dc\uac04\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774\ub54c, \ubaa8\ub4e0 \ud0dd\ubc30\ub97c \ubc30\ub2ec\ud558\ub294\ub370 \uac78\ub9ac\ub294 \ucd5c\uc18c \uc2dc\uac04\uc744 \uacc4\uc0b0\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ub3c4\uc2dc\uc758 \ud06c\uae30 R\uacfc C\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; R &le; 2000, 1 &le; C &le; 200)<\/p>\r\n\r\n<p>\ub2e4\uc74c R\uac1c \uc904\uc5d0\ub294, \uac01 \uce78\uc744 \ud1b5\uacfc\ud558\ub294\ub370 \ub4dc\ub294 \uc2dc\uac04\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774 \uc2dc\uac04\uc740 0\ubcf4\ub2e4 \ud06c\uac70\ub098 \uac19\uace0, 5000\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\uc740 \uc790\uc5f0\uc218\uc774\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c \uc904\uc5d0\ub294 \ubc30\ub2ec\ud574\uc57c \ud558\ub294 \ubb3c\ud488\uc758 \uc218 D (1 &le; D &le; 200000)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ub2e4\uc74c D\uac1c \uc904\uc5d0\ub294 \ubb3c\ud488\uc744 \ubc30\ub2ec\ud574\uc57c \ud558\ub294 \uacf3\uc758 \uc704\uce58\uc758 \uc88c\ud45c\uac00 \ubc30\ub2ec\ud574\uc57c \ud558\ub294 \uc21c\uc11c\ub300\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. \uac19\uc740 \uacf3\uc774 \uc5ec\ub7ec \ubc88 \uc8fc\uc5b4\uc9c8 \uc218\ub294 \uc788\ub2e4. \ud558\uc9c0\ub9cc, \uc5f0\uc18d\ud574\uc11c \uac19\uc740 \uacf3\uc744 \ubc30\ub2ec\ud574\uc57c \ud558\ub294 \uacbd\uc6b0\ub294 \uc5c6\ub2e4.&nbsp;<\/p>\r\n","output":"<p>\ubaa8\ub4e0 \ud0dd\ubc30\ub97c \ubc30\ub2ec\ud558\ub294\ub370 \uac00\uc7a5 \ube60\ub978 \uc2dc\uac04\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>\uc608\uc81c\uc758 \uacbd\uc6b0\uc5d0\ub294 \uc544\ub798\uc640 \uac19\uc774 \uc774\ub3d9\ud558\uba74 \ub41c\ub2e4.<\/p>\r\n\r\n<p>(1, 1), (2, 1), (3, 1), (3, 2), (3, 3), (2, 3), <strong>(1, 3)<\/strong>, (2, 3), <strong>(3, 3)<\/strong>, (2, 3), <strong>(2, 2)<\/strong><\/p>\r\n\r\n<p>\ucd1d \ubc30\ub2ec \uc2dc\uac04\uc740 1+2+1+0+1+2+2+2+1+2+3=17\uac00 \ub41c\ub2e4.<\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"2939","problem_lang":"1","title":"DOSTAVA","description":"<p>Little Ivica recently got a job delivering pizzas for the most popular pizzeria in town.&nbsp;<\/p>\r\n\r\n<p>At the start of his work day, he receives a list with the locations to which he needs to deliver pizzas, in order in which the locations are given.&nbsp;<\/p>\r\n\r\n<p>The city is divided into R&times;C cells. The rows are numbered 1 through R, columns 1 through C.&nbsp;<\/p>\r\n\r\n<p>From every cell, it is possible to move to neighbouring cells to the left and right. Moving up or down is only allowed in the first and last columns (columns 1 and C).&nbsp;<\/p>\r\n\r\n<p>The pizzeria is in the top left corner (1, 1) and this is the location Ivica starts from. Ivica takes with him all the pizzas he will deliver that day so he does not have to return to the pizzeria between deliveries or after the last delivery.&nbsp;<\/p>\r\n\r\n<p>For each location in the city, Ivica knows how much time he will spend every time he is in it (trying to get through the intersection, for example).&nbsp;<\/p>\r\n\r\n<p>Write a program that calculates the smallest amount of time for Ivica to deliver all the pizzas.<\/p>\r\n","input":"<p>The first line contains the integers R and C (1 &le; R &le; 2000, 1 &le; C &le; 200), the dimensions of the city.&nbsp;<\/p>\r\n\r\n<p>Each of the following R lines contains C integers. These are the times Ivica spends every time he enters a location. The times will be integers between 0 and 5000, inclusive.&nbsp;<\/p>\r\n\r\n<p>The next line contains an integer D (1 &le; D &le; 200000), the number of pizza deliveries that day. (No, it&#39;s not unrealistically large at all.)&nbsp;<\/p>\r\n\r\n<p>Each of the following D lines contains two integers A and B (1 &le; A &le; R, 1 &le; B &le; C), the location to which a pizza must be delivered. The pizzas are given in the order in which they must be delivered. No location will be given twice in a row.&nbsp;<\/p>\r\n","output":"<p>Output the smallest amount of time for Ivica to deliver all the pizzas.&nbsp;<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","hint":"<p>In the first, the shortest path goes through the following locations: (1, 1), (2, 1), (3, 1), (3, 2), (3, 3), (2, 3), (1, 3), (2, 3), (3, 3), (2, 3) and (2, 2).&nbsp;<\/p>\r\n\r\n<p>The locations in bold show where Mirko made deliveries.&nbsp;<\/p>\r\n\r\n<p>The total time for the deliveries is 1+2+1+0+1+2+2+2+1+2+3=17.<\/p>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]