2831. Vectors

At a geometry lesson Gerald was given a task: to get vector B out of vector A. Besides, the teacher permitted him to perform the following operations with vector A:

Turn the vector by 90 degrees clockwise. Add to the vector a certain vector C. Operations could be performed in any order any number of times.

Can Gerald cope with the task?

Input The first line contains integers x1 , y1 − the coordinates of the vector A (-108≤x1,y1≤108). The second and the third line contain in the similar manner vectors B and C (their coordinates are integers; their absolute value does not exceed 108).

Output Print “YES” (without the quotes) if it is possible to get vector B using the given operations. Otherwise print “NO” (without the quotes).

Examples Input

0 0 1 1 0 1

Output

YES

Input

0 0 1 1 1 1

Output

YES

Input

0 0 1 1 2 2

Output

NO

这道题的意思是对向量 A 可以进行 “顺时针旋转90°” 以及 “加上向量C” 这两种操作，操作次数与顺序不限，最后看能不能得出向量 B。 我的解法如下：

#include <stdio.h> typedef struct { int x; int y; }myVector; //向量加法 myVector vectorAdd(myVector A, myVector C) { myVector temp; temp.x = A.x + C.x; temp.y = A.y + C.y; return temp; } //向量旋转90° myVector vectorRotate(myVector A) { //旋转规则：(x, y) -> (y, -x) myVector temp; temp.x = A.y; temp.y = -A.x; return temp; } //比较两个向量的大小关系 //如果 A 的横坐标或纵坐标比 B 大，则定义 A > B int vectorCompare(myVector A, myVector B) { if (A.x == B.x && A.y == B.y) return 1; //相等返回 1 else if (A.x > B.x || A.y > B.y) return 2; //若 A > B，返回 2 else return 0; //否则返回 0 } int main() { myVector A, B, C; scanf("%d %d", &A.x, &A.y); scanf("%d %d", &B.x, &B.y); scanf("%d %d", &C.x, &C.y); myVector temp; int i = 0; if (A.x + A.y + C.x + C.y == 0 && B.x + B.y != 0) { //当 A 和 C 为零向量，但 B 不为零向量时 printf("NO"); return 0; } while (vectorCompare(A, B) == 0) { //旋转一次 temp = vectorRotate(A); if (vectorCompare(A, temp) == 1) { //旋转后为本身，则令 A 加上 C A = vectorAdd(A, C); continue; } //相加一次 temp = vectorAdd(temp, C); i++; // i 用来记录旋转次数 if (vectorCompare(temp, B) == 0) { if (i % 4 == 0) A = vectorAdd(A, C); //旋转四次需要将 A + C } else { A = temp; break; } } if (vectorCompare(A, B) == 1) printf("YES"); else if (vectorCompare(A, B) == 2) printf("NO"); return 0; }