There is an old tradition of keeping $4$ boxes of candies in the house in Cyberland. The numbers of candies are special if their arithmetic mean, their median and their range are all equal. By definition, for a set ${*x*_{1}, *x*_{2}, *x*_{3}, *x*_{4}}$ ($*x*_{1} ≤ *x*_{2} ≤ *x*_{3} ≤ *x*_{4}$) arithmetic mean is , median is and range is $*x*_{4} - *x*_{1}$. The arithmetic mean and median are not necessary integer. It is well-known that if those three numbers are same, boxes will create a "debugging field" and codes in the field will have no bugs.

For example, $1, 1, 3, 3$ is the example of $4$ numbers meeting the condition because their mean, median and range are all equal to $2$.

Jeff has $4$ special boxes of candies. However, something bad has happened! Some of the boxes could have been lost and now there are only $*n*$ ($0 ≤ *n* ≤ 4$) boxes remaining. The $*i*$-th remaining box contains $*a*_{*i*}$ candies.

Now Jeff wants to know: is there a possible way to find the number of candies of the $4 - *n*$ missing boxes, meeting the condition above (the mean, median and range are equal)?

Input

The first line of input contains an only integer $*n*$ ($0 ≤ *n* ≤ 4$).

The next $*n*$ lines contain integers $*a*_{*i*}$, denoting the number of candies in the $*i*$-th box ($1 ≤ *a*_{*i*} ≤ 500$).

Output

In the first output line, print "YES" if a solution exists, or print "NO" if there is no solution.

If a solution exists, you should output $4 - *n*$ more lines, each line containing an integer $*b*$, denoting the number of candies in a missing box.

All your numbers $*b*$ must satisfy inequality $1 ≤ *b* ≤ 10^{6}$. It is guaranteed that if there exists a positive integer solution, you can always find such $*b*$'s meeting the condition. If there are multiple answers, you are allowed to print any of them.

Given numbers $*a*_{*i*}$ may follow in any order in the input, not necessary in non-decreasing.

$*a*_{*i*}$ may have stood at any positions in the original set, not necessary on lowest $*n*$ first positions.

Note

For the first sample, the numbers of candies in $4$ boxes can be $1, 1, 3, 3$. The arithmetic mean, the median and the range of them are all $2$.

For the second sample, it's impossible to find the missing number of candies.

In the third example no box has been lost and numbers satisfy the condition.

You may output $*b*$ in any order.