Description

Take the ice house as the origin. The positions of the Sangetsusei are denoted by vectors $\vec{a}$, $\vec{b}$, $\vec{c}$.

By definition, $|\vec{a}|=r_1$, $|\vec{b}|=r_2$, $|\vec{c}|=r_3$.

Now Cirno assigns you the task of computing the destruction limit index $\sigma$.

$$\sigma=\min\{\vec{a}\cdot\vec{b}+\vec{b}\cdot\vec{c}+\vec{c}\cdot\vec{a}\}$$

Here, “$\cdot$” denotes the vector dot product.

Input Format

One line with three integers $r_1$, $r_2$, $r_3$, guaranteed that $r_1 \le r_2 \le r_3$.

Output Format

One line with one real number $\sigma$. (Keep one digit after the decimal point.)

3 4 5

-25.0

159 473 824 

-445561.0

Hint

Sample1 Explanation

The answer is minimized when $\cos\langle\vec{a},\vec{b}\rangle=0,\cos\langle\vec{b},\vec{c}\rangle=-\frac{4}{5},\cos\langle\vec{c},\vec{a}\rangle=-\frac{3}{5}$.

Required Math Knowledge

• Definition of dot product: $\vec{a}\cdot\vec{b}=|\vec{a}||\vec{b}|\times \cos\langle\vec{a},\vec{b}\rangle$
• Coordinate form of dot product: $(x_1,y_1)\cdot(x_2,y_2)=x_1x_2+y_1y_2$

Constraints

This problem uses bundled testdata.

• Subtask 1 ($20\%$): $r_1=r_2=r_3$
• Subtask 2 ($40\%$): $r_1,r_2,r_3 \le 10$
• Subtask 3 ($40\%$): $r_1,r_2,r_3 \le 10^9$

For $100\%$ of the testdata, $0 < r_1 \le r_2 \le r_3 \le 10^9$.

Translated by ChatGPT 5