문제
한국과학영재학교 기숙사에는 기숙사 입구와 2ドルN + 1$개의 방이 일직선으로 배치되어 있다. 왼쪽에서 $i$번째 방이 $i$번 방이고, 기숙사 입구는 1ドル$번 방 왼쪽에 있다. 입구와 $i$번 방 사이의 거리는 $x_i$미터이다. 그중에서, $N+1$번 방은 택배물 보관실로 사용되고 있다.
예성이는 벌점이 너무 많이 쌓여서 택배물 보관실의 택배물들을 배달하게 되었다. $M$개의 택배물이 택배물 보관실에 보관되어 있고, $j$번째 택배물은 $p_j$번 방으로 배달되어야 하며 무게는 $w_j$이다. 예성이의 목표는 택배물 보관실에서 출발해 모든 택배물을 배달한 후 다시 택배물 보관실로 돌아오는 것이다. 예성이가 택배물 보관실에서 택배물을 꺼내거나 택배물을 목적지에 놓을 때는 시간이 걸리지 않는다.
너무나도 강력한 예성이는 한 번에 여러 개의 택배물을 제한 없이 들 수 있지만, 처음에 모든 택배물을 가지고 출발할 필요는 없고, 일부는 보관실에 도중에 다시 들러서 꺼내올 수도 있다. 또 택배물을 배달하는 순서는 자유롭게 정할 수 있지만, 배달되어야 하는 목적지 이외의 장소에 잠시 놓아둘 수는 없다. 예성이가 택배물을 들고 있지 않을 때의 이동 속도는 초속 1ドル$미터인데, 현재 가지고 있는 택배물 무게의 총합이 $W$일 때는 이동 속도가 초속 $\cfrac{1}{1 + W}$미터로 감소한다.
예성이는 P=NP 문제를 증명하느라 시간이 없으므로, 목표를 달성하기 위해 최소 몇 초가 걸리는지 구해주자.
출력
문제의 정답을 출력한다. 주어진 조건 하에서 정답은 정수임이 보장된다.
제한
- 1ドル \leq N, M, w_j\leq 10^5$
- 1ドル \leq x_1 < x_2 < \cdots < x_{2N+1} \leq 3 \times 10^5$
- 1ドル \leq p_j \leq 2N+1$
[{"problem_id":"31989","problem_lang":"0","title":"\uae30\uc219\uc0ac \ud0dd\ubc30\ubb3c \ubc30\ub2ec","description":"<p>\ud55c\uad6d\uacfc\ud559\uc601\uc7ac\ud559\uad50 \uae30\uc219\uc0ac\uc5d0\ub294 \uae30\uc219\uc0ac \uc785\uad6c\uc640 $2N + 1$\uac1c\uc758 \ubc29\uc774 \uc77c\uc9c1\uc120\uc73c\ub85c \ubc30\uce58\ub418\uc5b4 \uc788\ub2e4. \uc67c\ucabd\uc5d0\uc11c $i$\ubc88\uc9f8 \ubc29\uc774 $i$\ubc88 \ubc29\uc774\uace0, \uae30\uc219\uc0ac \uc785\uad6c\ub294 $1$\ubc88 \ubc29 \uc67c\ucabd\uc5d0 \uc788\ub2e4. \uc785\uad6c\uc640 $i$\ubc88 \ubc29 \uc0ac\uc774\uc758 \uac70\ub9ac\ub294 $x_i$\ubbf8\ud130\uc774\ub2e4. \uadf8\uc911\uc5d0\uc11c, $N+1$\ubc88 \ubc29\uc740 \ud0dd\ubc30\ubb3c \ubcf4\uad00\uc2e4\ub85c \uc0ac\uc6a9\ub418\uace0 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc608\uc131\uc774\ub294 \ubc8c\uc810\uc774 \ub108\ubb34 \ub9ce\uc774 \uc313\uc5ec\uc11c \ud0dd\ubc30\ubb3c \ubcf4\uad00\uc2e4\uc758 \ud0dd\ubc30\ubb3c\ub4e4\uc744 \ubc30\ub2ec\ud558\uac8c \ub418\uc5c8\ub2e4. $M$\uac1c\uc758 \ud0dd\ubc30\ubb3c\uc774 \ud0dd\ubc30\ubb3c \ubcf4\uad00\uc2e4\uc5d0 \ubcf4\uad00\ub418\uc5b4 \uc788\uace0, $j$\ubc88\uc9f8 \ud0dd\ubc30\ubb3c\uc740 $p_j$\ubc88 \ubc29\uc73c\ub85c \ubc30\ub2ec\ub418\uc5b4\uc57c \ud558\uba70 \ubb34\uac8c\ub294 $w_j$\uc774\ub2e4. \uc608\uc131\uc774\uc758 \ubaa9\ud45c\ub294 \ud0dd\ubc30\ubb3c \ubcf4\uad00\uc2e4\uc5d0\uc11c \ucd9c\ubc1c\ud574 \ubaa8\ub4e0 \ud0dd\ubc30\ubb3c\uc744 \ubc30\ub2ec\ud55c \ud6c4 \ub2e4\uc2dc \ud0dd\ubc30\ubb3c \ubcf4\uad00\uc2e4\ub85c \ub3cc\uc544\uc624\ub294 \uac83\uc774\ub2e4. \uc608\uc131\uc774\uac00 \ud0dd\ubc30\ubb3c \ubcf4\uad00\uc2e4\uc5d0\uc11c \ud0dd\ubc30\ubb3c\uc744 \uaebc\ub0b4\uac70\ub098 \ud0dd\ubc30\ubb3c\uc744 \ubaa9\uc801\uc9c0\uc5d0 \ub193\uc744 \ub54c\ub294 \uc2dc\uac04\uc774 \uac78\ub9ac\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n\r\n<p>\ub108\ubb34\ub098\ub3c4 \uac15\ub825\ud55c \uc608\uc131\uc774\ub294 \ud55c \ubc88\uc5d0 \uc5ec\ub7ec \uac1c\uc758 \ud0dd\ubc30\ubb3c\uc744 \uc81c\ud55c \uc5c6\uc774 \ub4e4 \uc218 \uc788\uc9c0\ub9cc, \ucc98\uc74c\uc5d0 \ubaa8\ub4e0 \ud0dd\ubc30\ubb3c\uc744 \uac00\uc9c0\uace0 \ucd9c\ubc1c\ud560 \ud544\uc694\ub294 \uc5c6\uace0, \uc77c\ubd80\ub294 \ubcf4\uad00\uc2e4\uc5d0 \ub3c4\uc911\uc5d0 \ub2e4\uc2dc \ub4e4\ub7ec\uc11c \uaebc\ub0b4\uc62c \uc218\ub3c4 \uc788\ub2e4. \ub610 \ud0dd\ubc30\ubb3c\uc744 \ubc30\ub2ec\ud558\ub294 \uc21c\uc11c\ub294 \uc790\uc720\ub86d\uac8c \uc815\ud560 \uc218 \uc788\uc9c0\ub9cc, \ubc30\ub2ec\ub418\uc5b4\uc57c \ud558\ub294 \ubaa9\uc801\uc9c0 \uc774\uc678\uc758 \uc7a5\uc18c\uc5d0 \uc7a0\uc2dc \ub193\uc544\ub458 \uc218\ub294 \uc5c6\ub2e4. \uc608\uc131\uc774\uac00 \ud0dd\ubc30\ubb3c\uc744 \ub4e4\uace0 \uc788\uc9c0 \uc54a\uc744 \ub54c\uc758 \uc774\ub3d9 \uc18d\ub3c4\ub294 \ucd08\uc18d $1$\ubbf8\ud130\uc778\ub370, \ud604\uc7ac \uac00\uc9c0\uace0 \uc788\ub294 \ud0dd\ubc30\ubb3c \ubb34\uac8c\uc758 \ucd1d\ud569\uc774 $W$\uc77c \ub54c\ub294 \uc774\ub3d9 \uc18d\ub3c4\uac00 \ucd08\uc18d $\\cfrac{1}{1 + W}$\ubbf8\ud130\ub85c \uac10\uc18c\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc608\uc131\uc774\ub294 P=NP \ubb38\uc81c\ub97c \uc99d\uba85\ud558\ub290\ub77c \uc2dc\uac04\uc774 \uc5c6\uc73c\ubbc0\ub85c, \ubaa9\ud45c\ub97c \ub2ec\uc131\ud558\uae30 \uc704\ud574 \ucd5c\uc18c \uba87 \ucd08\uac00 \uac78\ub9ac\ub294\uc9c0 \uad6c\ud574\uc8fc\uc790.<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 \ub450 \uc815\uc218 $N, M$\uc774 \uacf5\ubc31\uc744 \uc0ac\uc774\uc5d0 \ub450\uace0 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc904\uc5d0 $2N + 1$\uac1c\uc758 \uc815\uc218 $x_1, x_2, \\cdots, x_{2N +1}$\uac00 \uacf5\ubc31\uc744 \uc0ac\uc774\uc5d0 \ub450\uace0 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uc138 \ubc88\uc9f8 \uc904\ubd80\ud130 $M$\uac1c\uc758 \uc904\uc5d0 \ud0dd\ubc30\ubb3c\ub4e4\uc758 \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc9c0\uba70, \uadf8 \uc911 $j$\ubc88\uc9f8 \uc904\uc5d0\ub294 \ub450 \uc815\uc218 $p_j$\uc640 $w_j$\uac00 \uacf5\ubc31\uc744 \uc0ac\uc774\uc5d0 \ub450\uace0 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\ubb38\uc81c\uc758 \uc815\ub2f5\uc744 \ucd9c\ub825\ud55c\ub2e4. \uc8fc\uc5b4\uc9c4 \uc870\uac74 \ud558\uc5d0\uc11c \uc815\ub2f5\uc740 \uc815\uc218\uc784\uc774 \ubcf4\uc7a5\ub41c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n\t<li>$1 \\leq N, M, w_j\\leq 10^5$<\/li>\r\n\t<li>$1 \\leq x_1 &lt; x_2 &lt; \\cdots &lt; x_{2N+1} \\leq 3 \\times 10^5$<\/li>\r\n\t<li>$1 \\leq p_j \\leq 2N+1$<\/li>\r\n<\/ul>\r\n"},{"problem_id":"31989","problem_lang":"1","title":"Delivering Parcels in the Dormitory","description":"<p>In the Korea Science Academy dormitory, there&#39;s an entrance and $2N + 1$ rooms arranged in a straight line. The rooms are numbered from left to right, with the entrance located to the left of room $1$. The distance between the entrance and room $i$ is $x_i$ meters. Among these rooms, room $N+1$ is being used as parcel storage.<\/p>\r\n\r\n<p>Due to accumulating many demerit points, Yeseong has been assigned to deliver parcels from the storage. There are $M$ parcels stored in the storage, and the $j$-th parcel must be delivered to room $p_j$ and weighs $w_j$. Yeseong&#39;s objective is to begin at the storage room, deliver all the parcels, and then return to the storage room. He can pick up a parcel from the storage room or put it at its delivery destination without spending any time.<\/p>\r\n\r\n<p>Yeseong is so strong that he can carry any number of parcels at once, but it is not necessary to carry all the parcels at the start; he can make multiple trips to the storage room to pick up additional parcels as needed. Also, parcels can be delivered in any order, but they cannot be temporarily left at places other than their delivery destination. Yeseong&#39;s walking speed is inversely proportional to the total weight of the parcels he is carrying. With no parcels, his speed is $1$ meter per second, and it decreases to $\\cfrac{1}{1 + W}$ meters per second when carrying a total weight of $W$.<\/p>\r\n\r\n<p>Since Yeseong has no time to spare, as he is busy proving the P=NP problem, let&#39;s help him how many seconds are required to achieve his objective.<\/p>\r\n","input":"<p>The first line contains two integers $N, M$ separated by a space.<\/p>\r\n\r\n<p>The second line contains $2N + 1$ integers $x_1, x_2, \\cdots, x_{2N +1}$ separated by spaces.<\/p>\r\n\r\n<p>From the third line onwards, information about the parcels is given, and on the $j$-th line, two integers $p_j$ and $w_j$ are given separated by a space.<\/p>\r\n","output":"<p>Print the answer to the problem. Under the given constraints, it is guaranteed that the answer will be an integer.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","limit":"<ul>\r\n\t<li>$1 \\leq N, M,&nbsp;w_j\\leq&nbsp;10^5$<\/li>\r\n\t<li>$1 \\leq x_1&nbsp;&lt;&nbsp;x_2 &lt; \\cdots &lt; x_{2N+1} \\leq 3&nbsp;\\times 10^5$<\/li>\r\n\t<li>$1 \\leq p_j \\leq 2N+1$<\/li>\r\n<\/ul>\r\n"}]