Mirko has found ~N~ chains in his attic. Each chain consists of some number of links, where each link has at most two adjacent links. Each link can be opened or closed, so it is possible to separate chains or connect them into a longer chain. Mirko would like to connect all chains into one huge chain, while opening and closing as few links as possible.

For example, if Mirko has only three chains, each consisting of only one link, he can open one of them, use it to connect the remaining two and close it:

Given the number of chains and the length of each chain, find the minimum number of links that Mirko has to open and close in order to bind them all in darkness one long chain.

Input Specification

The first line of input contains the positive integer ~N~ ~(2 \le N \le 500\,000)~, the number of chains.

The second line of input contains ~N~ positive integers ~L_i~ ~(1 \le L_i \le 1\,000\,000)~, the lengths of individual chains.

Output Specification

The first and only line of output must contain the required minimum number of links.

Sample Input 1

2
3 3

Sample Output 1

1

Explanation for Sample Output 1

Mirko can open the last link of the first chain, connect it with the first link of the second chain and close it.

Sample Input 2

3
1 1 1

Sample Output 2

1

Sample Input 3

5
4 3 5 7 9

Sample Output 3

3

Explanation for Sample Output 3

Here it is best to completely take apart the chain of length ~3~, using its three links to connect the remaining chains.