Radar Chart

A radar chart is a common way to show a game character's stats at a glance. A character has 8 stats. If the stats are $a\_1, a\_2, \cdots, a\_8$, the graph is an octagon, and the $k$-th vertex is $a\_k$ away from the origin in the direction of $45\times k$ degrees.

A radar chart shows how evenly the stats are distributed. If all stats are equal, the shape is a regular polygon. If one stat is much lower than the others, the polygon is concave. Many people try to make the graph a convex polygon, meaning every interior angle is at most $180°$, so that they can remove their weak spots.

Siru wants to turn his graph into a convex polygon, but raising stats is tedious. So he came up with a trick: change the order in which the stats are listed. For example, the list $\{6,7,7,8,9,10,11,13\}$ gives a concave polygon, but the list $\{7,6,7,8,9,10,11,13\}$ gives a convex polygon.

The order of the stats decides whether the polygon is concave or convex. Find the number of ways to arrange the stats so that the radar chart is a convex polygon.

The first line contains 8 integers $a\_1, a\_2, \cdots, a\_8$, the stats, separated by spaces. ($1 \leq a\_i \leq 10^4$)

Print the number of ways to arrange the 8 stats so that the radar chart is a convex polygon.