Problem Statement

Given are integers $N$, $M$, $S$, and a sequence of $N$ integers $A=(A_1,A_2,\cdots,A_N)$.

Consider making a sequence of $N$ non-negative real numbers $x=(x_1,x_2,\cdots,x_N)$ satisfying all of the following conditions:

• $0 \leq x_1 \leq x_2 \leq \cdots \leq x_N \leq M$,
• $\sum_{1 \leq i \leq N} x_i=S$.

Now, let us define the score of $x$ as $\sum_{1 \leq i \leq N} A_i \times x_i$. Find the maximum possible score of $x$.

Constraints

• $1 \leq N \leq 5000$
• $1 \leq M \leq 10^6$
• $1 \leq S \leq \min(N \times M,10^6)$
• $1 \leq A_i \leq 10^6$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M S
A_1 A_2 \cdots A_N

Constraints

Print the answer. Your output will be considered correct if its absolute or relative error is at most $10^{-6}$.