시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 128 MB 43 14 8 29.630%

문제

학생들은 프로그래밍 시간에 계속해서 떠들고 있다. 더 이상 참지 못한 조쌤은 자리를 박차고 애들을 잡기 위해 뛰기 시작했고 이와 동시에 떠들던 N명의 학생은 도망가기 시작했다.

현재 조쌤은 (BX, BY) 위치에 있다. 그리고 뛰기 시작한 조쌤은 t초 후 (BX+BVX*t, BY+BVY*t) 위치에 있게 된다. 즉 조쌤은 초당 (BVX, BVY) 방향으로 뛰고 있는 것이다.

N명의 학생 역시 현재 (Xi, Yi)에 위치하고 있고 t(t ≥ 0)초 후 (Xi+VXi*t, Yi+VYi*t) 위치에 있게 된다.

조쌤은 현재 자신 위치에서 반경이 R인 원 안에 있는 아이들은 모조리 잡을 수 있다. 하지만 위의 조건을 살펴보면 현재 아이들과 조쌤 모두 뛰는 상황이기에 시간마다 아이들을 잡을 수 있는 숫자가 변한다. 조쌤은 한 번 잡고나면 잡히지 않은 아이들은 모두 도망간 상태기 때문에 단 한번의 기회에 최대한 많은 아이들을 잡고 싶다.

문제는 조쌤과 학생들의 위치 및 뛰는 방향이 주어지면 한 번에 얼마나 많은 학생을 잡을 수 있는지 구하는 것이다. 물론, 최대한 많이 잡을 수 있는 시간이 정수가 아닌 소수일 수도 있다.

입력

첫 줄에는 학생의 수 N(1 ≤ N ≤ 50,000)과 조쌤이 잡을 수 있는 반경 R(1 ≤ R ≤ 2,500), 그리고 조쌤의 위치를 나타내는 BX, BY(-1,000 ≤ BX, BY ≤ 1,000)와 조쌤이 뛰는 방향을 나타내는 BVX, BVY(-100 ≤ BVX, BVY ≤ 100)가 공백으로 구분되어 주어진다. 두 번째 줄부터 N+1번째 줄까지는 각 학생의 정보가 주어지는데 각 줄에는 학생의 초기 위치 Xi, Yi와 뛰는 방향 VXi, VYi(-1,000 ≤ Xi, Yi, VXi, VYi ≤ 1,000)가 공백으로 구분되어 주어진다. 입력되는 모든 수는 정수이다.

출력

첫 줄에 조쌤이 한 번에 잡을 수 있는 최대 학생 숫자를 출력한다. 실수 오차 조정을 위해 학생과 조교 사이의 거리가 R±0.0001이라면 잡을 수 있다고 한다.

예제 입력 1

3 1 0 0 0 2
0 -3 0 4
1 2 -1 1
1 -2 2 -1

예제 출력 1

2

힌트

1.5초의 시간이 흐른 후 조쌤은 (0, 3)에 위치해 있고 각 학생은 (0, 3), (-0.5, 3.5), (4, -3.5)에 위치하여 있다. 즉 반경 1 안에 있는 1, 2번 학생을 조쌤은 잡을 수 있고 이것이 한 번에 잡을 수 있는 최대 학생 수가 된다.
[{"problem_id":"1177","problem_lang":"0","title":"\uc870\uc324\ud3ec\uc2a4","description":"<p>\ud559\uc0dd\ub4e4\uc740 \ud504\ub85c\uadf8\ub798\ubc0d \uc2dc\uac04\uc5d0 \uacc4\uc18d\ud574\uc11c \ub5a0\ub4e4\uace0 \uc788\ub2e4. \ub354 \uc774\uc0c1 \ucc38\uc9c0 \ubabb\ud55c \uc870\uc324\uc740 \uc790\ub9ac\ub97c \ubc15\ucc28\uace0 \uc560\ub4e4\uc744 \uc7a1\uae30 \uc704\ud574 \ub6f0\uae30 \uc2dc\uc791\ud588\uace0 \uc774\uc640 \ub3d9\uc2dc\uc5d0 \ub5a0\ub4e4\ub358 N\uba85\uc758 \ud559\uc0dd\uc740 \ub3c4\ub9dd\uac00\uae30 \uc2dc\uc791\ud588\ub2e4.<\/p>\r\n<p>\ud604\uc7ac \uc870\uc324\uc740 (BX, BY) \uc704\uce58\uc5d0 \uc788\ub2e4. \uadf8\ub9ac\uace0 \ub6f0\uae30 \uc2dc\uc791\ud55c \uc870\uc324\uc740 t\ucd08 \ud6c4 (BX+BVX*t, BY+BVY*t) \uc704\uce58\uc5d0 \uc788\uac8c \ub41c\ub2e4. \uc989 \uc870\uc324\uc740 \ucd08\ub2f9 (BVX, BVY) \ubc29\ud5a5\uc73c\ub85c \ub6f0\uace0 \uc788\ub294 \uac83\uc774\ub2e4.<\/p>\r\n<p>N\uba85\uc758 \ud559\uc0dd \uc5ed\uc2dc \ud604\uc7ac (Xi, Yi)\uc5d0 \uc704\uce58\ud558\uace0 \uc788\uace0 t(t &ge; 0)\ucd08 \ud6c4 (Xi+VXi*t, Yi+VYi*t) \uc704\uce58\uc5d0 \uc788\uac8c \ub41c\ub2e4.<\/p>\r\n<p>\uc870\uc324\uc740 \ud604\uc7ac \uc790\uc2e0 \uc704\uce58\uc5d0\uc11c \ubc18\uacbd\uc774 R\uc778 \uc6d0 \uc548\uc5d0 \uc788\ub294 \uc544\uc774\ub4e4\uc740 \ubaa8\uc870\ub9ac \uc7a1\uc744 \uc218 \uc788\ub2e4. \ud558\uc9c0\ub9cc \uc704\uc758 \uc870\uac74\uc744 \uc0b4\ud3b4\ubcf4\uba74 \ud604\uc7ac \uc544\uc774\ub4e4\uacfc \uc870\uc324 \ubaa8\ub450 \ub6f0\ub294 \uc0c1\ud669\uc774\uae30\uc5d0 \uc2dc\uac04\ub9c8\ub2e4 \uc544\uc774\ub4e4\uc744 \uc7a1\uc744 \uc218 \uc788\ub294 \uc22b\uc790\uac00 \ubcc0\ud55c\ub2e4. \uc870\uc324\uc740 \ud55c \ubc88 \uc7a1\uace0\ub098\uba74 \uc7a1\ud788\uc9c0 \uc54a\uc740 \uc544\uc774\ub4e4\uc740 \ubaa8\ub450 \ub3c4\ub9dd\uac04 \uc0c1\ud0dc\uae30 \ub54c\ubb38\uc5d0 \ub2e8 \ud55c\ubc88\uc758 \uae30\ud68c\uc5d0 \ucd5c\ub300\ud55c \ub9ce\uc740 \uc544\uc774\ub4e4\uc744 \uc7a1\uace0 \uc2f6\ub2e4.<\/p>\r\n<p>\ubb38\uc81c\ub294 \uc870\uc324\uacfc \ud559\uc0dd\ub4e4\uc758 \uc704\uce58 \ubc0f \ub6f0\ub294 \ubc29\ud5a5\uc774 \uc8fc\uc5b4\uc9c0\uba74 \ud55c \ubc88\uc5d0 \uc5bc\ub9c8\ub098 \ub9ce\uc740 \ud559\uc0dd\uc744 \uc7a1\uc744 \uc218 \uc788\ub294\uc9c0 \uad6c\ud558\ub294 \uac83\uc774\ub2e4. \ubb3c\ub860, \ucd5c\ub300\ud55c \ub9ce\uc774 \uc7a1\uc744 \uc218 \uc788\ub294 \uc2dc\uac04\uc774 \uc815\uc218\uac00 \uc544\ub2cc \uc18c\uc218\uc77c \uc218\ub3c4 \uc788\ub2e4.<\/p>","input":"<p>\uccab \uc904\uc5d0\ub294 \ud559\uc0dd\uc758 \uc218 N(1 &le; N &le; 50,000)\uacfc \uc870\uc324\uc774 \uc7a1\uc744 \uc218 \uc788\ub294 \ubc18\uacbd R(1 &le; R &le; 2,500), \uadf8\ub9ac\uace0 \uc870\uc324\uc758 \uc704\uce58\ub97c \ub098\ud0c0\ub0b4\ub294 BX, BY(-1,000 &le; BX, BY &le; 1,000)\uc640 \uc870\uc324\uc774 \ub6f0\ub294 \ubc29\ud5a5\uc744 \ub098\ud0c0\ub0b4\ub294 BVX, BVY(-100 &le; BVX, BVY &le; 100)\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. \ub450 \ubc88\uc9f8 \uc904\ubd80\ud130 N+1\ubc88\uc9f8 \uc904\uae4c\uc9c0\ub294 \uac01 \ud559\uc0dd\uc758 \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc9c0\ub294\ub370 \uac01 \uc904\uc5d0\ub294 \ud559\uc0dd\uc758 \ucd08\uae30 \uc704\uce58 Xi, Yi\uc640 \ub6f0\ub294 \ubc29\ud5a5 VXi, VYi(-1,000 &le; Xi, Yi, VXi, VYi &le; 1,000)\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. \uc785\ub825\ub418\ub294 \ubaa8\ub4e0 \uc218\ub294 \uc815\uc218\uc774\ub2e4.<\/p>","output":"<p>\uccab \uc904\uc5d0 \uc870\uc324\uc774 \ud55c \ubc88\uc5d0 \uc7a1\uc744 \uc218 \uc788\ub294 \ucd5c\ub300 \ud559\uc0dd \uc22b\uc790\ub97c \ucd9c\ub825\ud55c\ub2e4. \uc2e4\uc218 \uc624\ucc28 \uc870\uc815\uc744 \uc704\ud574 \ud559\uc0dd\uacfc \uc870\uad50 \uc0ac\uc774\uc758 \uac70\ub9ac\uac00 R&plusmn;0.0001\uc774\ub77c\uba74 \uc7a1\uc744 \uc218 \uc788\ub2e4\uace0 \ud55c\ub2e4.<\/p>","hint":"1.5\ucd08\uc758 \uc2dc\uac04\uc774 \ud750\ub978 \ud6c4 \uc870\uc324\uc740 (0, 3)\uc5d0 \uc704\uce58\ud574 \uc788\uace0 \uac01 \ud559\uc0dd\uc740 (0, 3), (-0.5, 3.5), (4, -3.5)\uc5d0 \uc704\uce58\ud558\uc5ec \uc788\ub2e4. \uc989 \ubc18\uacbd 1 \uc548\uc5d0 \uc788\ub294 1, 2\ubc88 \ud559\uc0dd\uc744 \uc870\uc324\uc740 \uc7a1\uc744 \uc218 \uc788\uace0 \uc774\uac83\uc774 \ud55c \ubc88\uc5d0 \uc7a1\uc744 \uc218 \uc788\ub294 \ucd5c\ub300 \ud559\uc0dd \uc218\uac00 \ub41c\ub2e4.\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"1177","problem_lang":"1","title":"Cattle Bruisers","description":"<p>Canmuu is out for revenge after being utterly defeated by Bessie in paintball and has challenged Bessie to a video game.<\/p>\r\n\r\n<p>In this game, Bessie starts out at point (BX, BY) in the coordinate grid (-1,000 &lt;= BX &lt;= 1,000; -1000 &lt;= BY &lt;= 1,000), and tries to escape, starting at time 0. She moves continuously at a velocity of (BVX, BVY) units\/second (-100 &lt;= BVX &lt;= 100; -100 &lt;= BVY &lt;= 100). Thus, at time 1 she will be at point (BX + BVX, BY + BVY); at time 1.5 she will be at (BX + 1.5*BVX, BY + 1.5*BVY).<\/p>\r\n\r\n<p>Unfortunately, Canmuu has sent N (1 &lt;= N &lt;= 50,000) cattle bruisers to pursue Bessie. &nbsp;At time t=0, cattle bruiser i is at position (X_i, Y_i) (-1,000 &lt;= X_i &lt;= 1,000; -1,000 &lt;= Y_i &lt;= 1,000) with velocity (VX_i, VY_i) units\/second (-1,000 &lt;= VX_i &lt;= 1,000; -1,000 &lt;= VY_i &lt;= 1,000).<\/p>\r\n\r\n<p>Each cattle bruiser carries a &quot;proximity&quot; weapon to fire at Bessie; the weapon can hurt Bessie when the cattle bruiser is no further than R (1 &lt;= R &lt;= 2,500) units from her.<\/p>\r\n\r\n<p>Bessie has a shield to protect herself from these attacks. However, she does not want to waste any of her shield&#39;s power, so she would like to know the maximum number of cattle bruisers within firing range for any (potentially non-integer) time t &gt;= 0.<\/p>\r\n\r\n<p>In order to avoid precision errors with real numbers, it is guaranteed that the answer produced will be the same whether the attack range is decreased to R-0.0001 or increased to R+0.0001.<\/p>\r\n","input":"<p>* Line 1: Six space-separated integers: N, R, BX, BY, BVX, and BVY<\/p>\r\n\r\n<p>* Lines 2..N+1: Line i+1 contains four space-separated integers: X_i, Y_i, VX_i, and VY_i<\/p>\r\n","output":"<p>* Line 1: Print a single integer denoting the maximum number of cattle bruisers within attack range at any point in time.<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]