P16193 [ROIR 2014 Day 1] POBEDA-2014

As everyone knows, modern graphics cards draw images by assembling triangles. The POBEDA-2014 graphics card is no exception: it can display only four orientations of isosceles right triangles, as shown in the figure below. The graphics card cannot change the orientation of these triangles.  For each triangle, the length of each leg of the right angle is $1$ centimeter. In each clock cycle, the graphics card can display at most $a_i$ triangles of type $i$. Your task is to compute the maximum possible side length of a square that the graphics card can draw within one clock cycle. Note that the sides of this square must be parallel to the sides of the monitor. Write a program to solve this problem.

The first line of the input contains four integers separated by spaces: $a_1, a_2, a_3, a_4\ (0 \le a_i \le 10^{18})$. Note that the input values may exceed the range of 32-bit integers.

N/A

The following figure is an illustration of the first sample, for reference.  ### Scoring For the $50$-point testdata, $a_1, a_2, a_3, a_4 \le 100\,000$. Translation source: GPT 4.1 mini. Translated by ChatGPT 5