An equilateral triangle with side 101 is placed on a plane so that one of its sides is horizontal and the triangle is above it. It is divided into smaller equilateral triangles with side 1 by segments parallel to its sides. All sides of these smaller triangles are colored red (including the entire border of the large triangle). An equilateral triangle on a plane is called a "mirror" triangle if its sides are parallel to the sides of the original triangle, but it lies below its horizontal side. What is the smallest number of contours of mirror triangles needed to cover all the red segments? (Mirror triangles may overlap and extend beyond the original triangle.) Proposed by Dmitry Shiryayev