CWMO 2017 Problem 5

Let $a_1,a_2,\cdots ,a_9$ be $9$ positive integers (not necessarily distinct) satisfying: for all $1\le i<j<k\le 9$ , there exists $l (1\le l\le 9)$ distinct from $i,j$ and $j$ such that $a_i+a_j+a_k+a_l=100$ . Find the number of $9$ -tuples $(a_1,a_2,\cdots ,a_9)$ satisfying the above conditions.