Maximum of minima P38906

Write a function

    long long maxmin(const vector<long long>& V);

that returns $$\max_{0 \le i < j < n} \left\{ \min(V[i], V[j]) \times (j - i) \right\} \enspace .$$

For instance, the answer for $[9, 7, 4, 1]$ is 8, corresponding to the numbers 9 and 4, which are at distance 2. As another example, the answer for a vector with eleven $10^9$ is $10^{10}$.

Precondition

@V@ has between 2 and $10^5$ numbers, all between 0 and $10^9$.

Observation

The expected solution has cost $\Theta(V.size())$, with a small constant.

Observation

You only need to submit the required procedure; your main program will be ignored.