Cow Baseball

Farmer John's $N$ cows ($3 \le N \le 1000$) stand in a row on the number line, and no two of them stand at the same position. They are practicing throws with a baseball before an important game against the cows on the neighboring farm.

While Farmer John watches, three cows $(X, Y, Z)$ complete two successful throws. Cow $X$ throws the ball to cow $Y$, who stands to the right of $X$, and then cow $Y$ throws the ball to cow $Z$, who stands to the right of $Y$. The second throw travels at least as far as the first one and no more than twice as far. Count the triples $(X, Y, Z)$ that Farmer John could have been watching.

• Line 1: the number of cows, $N$.
• Lines 2 to $N + 1$: each line holds the position of one cow, an integer between $0$ and $100\,000\,000$.

• Line 1: the number of triples $(X, Y, Z)$ where $Y$ is to the right of $X$, $Z$ is to the right of $Y$, and the distance from $Y$ to $Z$ is at least the distance from $X$ to $Y$ and at most twice that distance.

In the first example five cows stand at positions $3$, $1$, $10$, $7$, $4$. The four triples that work are the cows at positions $(1, 3, 7)$, $(1, 4, 7)$, $(4, 7, 10)$, $(1, 4, 10)$.