Mission Control operates an experimental power grid: a relay station sits at every integer coordinate (x, y) on an infinite plane, and the station at (x, y) generates exactly |x| + |y| gigawatts. Engineers want to enclose the hub at the origin with a square containment fence whose sides are parallel to the axes and whose corners are (p, p), (p, -p), (-p, p) and (-p, -p) for some integer p >= 0. The fence encloses every relay station with -p <= x <= p and -p <= y <= p, including stations sitting exactly on the boundary.

Given the total generation capacity that must be captured, find the minimum possible perimeter of a fence that captures at least that much power in total, summed over every enclosed station (boundary included).

Input format

A single line containing one integer need, the required total generation capacity.

Output format

A single integer: the minimum perimeter of a valid fence.

Constraints

• 1 <= need <= 10^15
• The answer fits comfortably in a 64-bit integer.

1

8

100

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