Let positive integers $a_1, a_2, \cdots, a_{31}, b_1, b_2, \cdots, b_{31}$ satisfy the following conditions: - $a_1 < a_2 < a_3 < \cdots < a_{31}$ - $b_1 < b_2 < b_3 < \cdots < b_{31}$ - $a_1 + a_2+a_3+\cdots + a_{31} = b_1 + b_2 + b_3 + \cdots + b_{31}=2015$ Find the maximum value of $S=\mid a_1 - b_1 \mid + \mid a_2 - b_2 \mid + \cdots + \mid a_{31}-b_{31}\mid$.