codeforces Div#432 B Arpa and an exam about geometry（技巧）

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 ax, ay, bx, by, cx, cy (|ax|, |ay|, |bx|, |by|, |cx|, |cy| ≤ 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

0 1 1 1 1 0

output

Yes

input

1 1 0 0 1000 1000

output

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.

 【题解】

大致题意：三个点a,b,c，问能否在平面上找到一点O，使得aOb角旋转一定的度数后可以与bOc重合，即a点与b点重合，b点与c点重合。

经过分析，要重合，只能是ab长等于bc长，同时三个点不在同一条直接上就可以了。

【AC代码】

#include<iostream>#include<cstdio>#include<algorithm>#include<cstring>using namespace std;typedef __int64 ll;ll x1,x2,x3,y1,y2,y3;ll check(ll a,ll b,ll c,ll d){    return (a-c)*(a-c)+(b-d)*(b-d);}int main(){    while(~scanf("%I64d%I64d%I64d%I64d%I64d%I64d",&x1,&y1,&x2,&y2,&x3,&y3))    {        ll xx1=x2-x1;        ll xx2=x3-x1;        ll yy1=y2-y1;        ll yy2=y3-y1;        if((check(x1,y1,x2,y2)==check(x2,y2,x3,y3))&&(xx1*yy2 != xx2*yy1))            printf("Yes\n");        else            printf("No\n");    }    return 0;}