Define a sequence of positive integers $s_1, s_2, . . . , s_{10}$ to be $terrible$ if the following conditions are satisfied for any pair of positive integers $i$ and $j$ satisfying $1 \le i < j \le 10$: - $s_i > s_j$ - $j - i + 1$ divides the quantity $s_i + s_{i+1} + \cdots + s_j$ Determine the minimum possible value of $s_1 + s_2 + \cdots + s_{10}$ over all terrible sequences.