CONO-SUR 2010 Problem 2

On a line, $44$ points are marked and numbered $1, 2, 3,…,44$ from left to right. Various crickets jump around the line. Each starts at point $1$ , jumping on the marked points and ending up at point $44$ . In addition, each cricket jumps from a marked point to another marked point with a greater number. When all the crickets have finished jumping, it turns out that for pair $i, j$ with ${1}\leq{i}<{j}\leq{44}$ , there was a cricket that jumped directly from point $i$ to point $j$ , without visiting any of the points in between the two. Determine the smallest number of crickets such that this is possible.