Sabotage

Farmer Paul's plan is to disconnect a contiguous block of milking machines, but not the first or the last one.

There are $N$ machines in a row. Machine $i$ produces $M_i$ units of milk ($3 \le N \le 100\,000$, $1 \le M_i \le 10\,000$). Paul may remove machines $i$ through $j$ with $2 \le i \le j \le N-1$. He must remove at least one machine. After removal, what is the minimum possible average production of the machines that remain?

Farmer John wants that minimum average if Paul's plot succeeds.

Line 1 contains the integer $N$.

The next $N$ lines each contain $M_i$ for machine $i$.

Print the minimum achievable average, rounded to three digits after the decimal point, with exactly three digits after the decimal point.