NL-BXMO-TST 2017 Problem 1

Let $n$ be an even positive integer. A sequence of $n$ real numbers is called complete if for every integer $m$ with $1 \leq m \leq n$ either the sum of the first $m$ terms of the sum or the sum of the last $m$ terms is integral. Determine the minimum number of integers in a complete sequence of $n$ numbers.