In an alternate universe, every person has a three-letter name, and each letter must have a distinct reading. For example, "JWS" is a valid name, but "JW" is not because it has only two letters, and "JWJ" is not a valid name because two of the letters are same.

If there are three people whose names have a magical characteristic, we call them a "name group". The characteristics of a name group are as follows: you can choose three different letters such that each letter is contained in the names of at least two people in the group.

For example, if the first person is named "ACD", the second person is named "ABE", and the third person is named "BCF", then selecting "A" would include the first two people, selecting "C" would include the first and third people, and selecting "B" would include the second and third people. (Only the inclusion of a letter is necessary, not the position of the letter in the name.)

That is, for the letters 'A', 'B' and 'C', each letter is contained in the names of at least two people.

Note: each person can only be in one name group, and different people can have the same name.

Now, you have a library of unique letters, and each letter can be used times, with the total number of uses of all letters guaranteed to be a multiple of 3. You can create people names with them, where is the sum of all . Please determine the maximum number of name groups you can create. If it is impossible to create valid name groups, output -1.

The first line contains an integer  , representing the number of unique letters in the library.

The second line contains  positive integers,  , representing the number of times each letter can be used. The sum of all  is guaranteed to be a multiple of 3.

Output a single integer, representing the maximum number of name groups you can create.

3
4 4 4

1

A total of 4 people with the same name can be created, but since a name group needs to include 3 people,
there can only be one name group.

1
9

-1

6
2 2 2 1 1 1

1

This is the example in the problem statement.

8
4 3 3 3 2 1 1 1

2