Arpa and an exam about geometry（codeforces 851B）

Arpa and an exam about geometry

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Arpa is taking a geometry exam. Here is the last problem of the exam.

You are given three points a, b, c.

Find a point and an angle such that if we rotate the page around the point by the angle, the new position of a is the same as the old position of b, and the new position of b is the same as the old position of c.

Arpa is doubting if the problem has a solution or not (i.e. if there exists a point and an angle satisfying the condition). Help Arpa determine if the question has a solution or not.

Input

The only line contains six integers a_x, a_y, b_x, b_y, c_x, c_y (|a_x|, |a_y|, |b_x|, |b_y|, |c_x|, |c_y| ≤ 10⁹). It's guaranteed that the points are distinct.

Output

Print "Yes" if the problem has a solution, "No" otherwise.

You can print each letter in any case (upper or lower).

Examples

Input

Copy

0 1 1 1 1 0

Output

Copy

Yes

Input

Copy

1 1 0 0 1000 1000

Output

Copy

No

Note

In the first sample test, rotate the page around (0.5, 0.5) by .

In the second sample test, you can't find any solution.

#include<iostream>
#include<cstdio>
#include<cstring>
#include<string>
#include<cmath>
using namespace std;
struct Point{
    int x,y;
    Point(){}
    Point(int a,int b):x(a),y(b){}
    inline void input(){
        scanf("%d%d", &x, &y);
    }
    Point operator-(const Point &a)const{
        return Point(x - a.x, y - a.y);
    }
    bool operator==(const Point &a)const{
        if((x - a.x)==0 && (y - a.y)==0) return 1;
        else return 0;
    }
    Point operator/(const double &a){
        return Point(x/a, y/a);
    }
    bool pdk(const Point &a){
        return (1ll*x * a.y - 1ll*y * a.x)==0;
    }
    void output(){
        printf("x = %d  y = %d\n", x, y);
    }
    long long dis(){
        return 1ll*x*x + 1ll*y*y;
    }
};
struct Line{
    Point s,e;
    Line(){}
    Line(const Point &a, const Point &b):s(a),e(b){}
    Line(const Line &a){
        s = a.s, e = a.e;
    }
};
int main(){
    Point a,b,c;
    a.input();
    b.input();
    c.input();
    if( (b-a).pdk(c-b) || (b-a).dis()!= (c-b).dis()) puts("No");
    else puts("Yes");
    return 0;
}

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