P6299 Difference

Define the difference measure between integers $p,q,r,s$ and the given integers $a,b,c,d$ as $$M=\Big|\left(a^2+b^2\right)\left(p^2+q^2\right)+\left(c^2+d^2\right)\left(r^2+s^2\right)+2\big(ac+bd\big)\big(pr-qs\big)+2\big(bc-ad\big)\big(ps+qr\big)\Big|$$ Your task is to find the smallest non-zero value of the difference measure $M$, and one set of $p,q,r,s$ that achieves this smallest non-zero value. It is guaranteed that the smallest non-zero value of $M$ exists and is less than $2^{63}$. It is also guaranteed that there exists a set of $p,q,r,s$ with all absolute values less than $2^{63}$ such that $M$ attains the smallest non-zero value.

Input one line with four integers $a,b,c,d$, as described above.

Output one line with five integers $p,q,r,s,M$, representing a set of $p,q,r,s$ that makes the difference measure $M$ reach its smallest non-zero value, and the value of $M$ at that time.

### Sample Explanation #1 Obviously, when $a=1,b=9,c=2,d=6$, the difference measure $M$ must be even, so $M$ cannot take any non-zero value smaller than $2$. ### Constraints | Test Point ID | Special Property | |:-:|:-:| | $1$ | $c=d=0$ | | $2$ | $a=c=0$ | | $3$ | $b=d=0$ | | $4$ | $ad=bc$ | | $5$ | $\vert a\vert,\vert b\vert,\vert c\vert,\vert d\vert\le10$ | | $6\sim10$ | None | For $100\%$ of the testdata, $\vert a\vert,\vert b\vert,\vert c\vert,\vert d\vert\le10^9$. ### Scoring Method **You must ensure that the number of values you output for each test point is** $5$ **and that** $\vert p\vert,\vert q\vert,\vert r\vert,\vert s\vert,\vert M\vert