Minimum and Maximum

Chef has a $permutation$ $P_1, P_2, \ldots, P_N$ of integers $1$ through $N$. He needs you to find the value of the sum $$S = \sum\limits_{i=1}^{N} \sum\limits_{j=i}^{N} \mathrm{getMin}\,(i, j) \; \wedge \; \mathrm{getMax}\,(i, j) \,,$$ where $\wedge$ denotes the bitwise AND operation and $$\mathrm{getMin}\,(i, j) = \mathrm{min}\,(P_i, P_{i+1}, \ldots, P_{j-1}, P_j) \,,$$ $$\mathrm{getMax}\,(i, j)