You are given a sequence of $N$ positive integers $A = (A_1, A_2, \dots ,A_N)$. Takahashi repeats the following operation until $A$ contains one or fewer positive elements:

• Sort $A$ in descending order. Then, decrease both $A_1$ and $A_2$ by $1$.

Find the number of times he performs this operation.

The input is given from Standard Input in the following format:

$N$

$A_1$ $A_2$ $\cdots$ $A_N$

Print the answer.

• $2 \leq N \leq 100$
• $1 \leq A_i \leq 100$
• All input values are integers.

The process goes as follows:

• After the 1st operation, $A$ is $(2, 2, 2, 1)$.
• After the 2nd operation, $A$ is $(1, 1, 2, 1)$.
• After the 3rd operation, $A$ is $(1, 0, 1, 1)$.
• After the 4th operation, $A$ is $(0, 0, 1, 0)$. $A$ no longer contains more than one positive elements, so the process ends here.