Chef and Circle

Chef has $m$ numbers $n_1,n_2,…,n_m$. He wants to know if it is possible to permute the numbers in a circular arrangement in such a way that for every three consecutive numbers, the middle number is strictly less than the sum of the other two numbers. As an example, consider the array $[1,4,5,6,7,8]$. For this array, the permutation on the left is valid, while the one on the right is not, as $5