Counting problem (4)

Given a sequence of $n$ integer numbers $x_1 \dots x_n$, count how many $i$’s, with $1 \le i \le n$, follow the property

$$\vert \{ j : 1 \le j < i \wedge x_j < x_i \} \vert = \vert \{ j : 1 \le j < i \wedge x_j > x_i \} \vert \enspace .$$

Input

The input consists of several cases. Each case begins with $n$, followed by the $n$ integer numbers $x_1 \dots x_n$. Assume $0 \le n \le 10^5$.

Output

For each case, print the number of indices $i$ that fulfill the condition above.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T11:19:42.649Z

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