Laboratory Work
Contest: Codeforces Round 468 (Div. 2, based on Technocup 2018 Final Round)
Difficulty rating: 1700
Tags: implementation, math

Anya and Kirill are doing a physics laboratory work. In one of the tasks they have to measure some value n times, and then compute the average value to lower the error.

Kirill has already made his measurements, and has got the following integer values: x1, x2, ..., xn. It is important that the values are close to each other, namely, the difference between the maximum value and the minimum value is at most 2.

Anya does not want to make the measurements, however, she can't just copy the values from Kirill's work, because the error of each measurement is a random value, and this coincidence will be noted by the teacher. Anya wants to write such integer values y1, y2, ..., yn in her work, that the following conditions are met:

- the average value of x1, x2, ..., xn is equal to the average value of y1, y2, ..., yn;
- all Anya's measurements are in the same bounds as all Kirill's measurements, that is, the maximum value among Anya's values is not greater than the maximum value among Kirill's values, and the minimum value among Anya's values is not less than the minimum value among Kirill's values;
- the number of equal measurements in Anya's work and Kirill's work is as small as possible among options with the previous conditions met. Formally, the teacher goes through all Anya's values one by one, if there is equal value in Kirill's work and it is not strike off yet, he strikes off this Anya's value and one of equal values in Kirill's work. The number of equal measurements is then the total number of strike off values in Anya's work.

Help Anya to write such a set of measurements that the conditions above are met.

Input format:
The first line contains a single integer n (1 ≤ n ≤ 100 000) — the numeber of measurements made by Kirill.

The second line contains a sequence of integers x1, x2, ..., xn ( - 100 000 ≤ xi ≤ 100 000) — the measurements made by Kirill. It is guaranteed that the difference between the maximum and minimum values among values x1, x2, ..., xn does not exceed 2.

Output format:
In the first line print the minimum possible number of equal measurements.

In the second line print n integers y1, y2, ..., yn — the values Anya should write. You can print the integers in arbitrary order. Keep in mind that the minimum value among Anya's values should be not less that the minimum among Kirill's values, and the maximum among Anya's values should be not greater than the maximum among Kirill's values.

If there are multiple answers, print any of them.

Constraints:
Time limit: 1.0 s
Memory limit: 256.0 MB

Note:
In the first example Anya can write zeros as here measurements results. The average value is then equal to the average value of Kirill's values, and there are only two equal measurements.

In the second example Anya should write two values 100 and one value 101 (in any order), because it is the only possibility to make the average be the equal to the average of Kirill's values. Thus, all three measurements are equal.

In the third example the number of equal measurements is 5.

Example input:
6
-1 1 1 0 0 -1

Example output:
2
0 0 0 0 0 0

Example input:
3
100 100 101

Example output:
3
101 100 100

Editorial:
The average value of Anya measurements should be equal to the average value of Kirill's measurements, so the sum of all Anya measurements should be equal to the sum of all Kirill dimensions.
Let the minimum number in the Kirill's measurements is min and the maximum — max. Then, if (max - min) is less than or equal to one, Anya will not be able to write down any measurements that Kirill do not have, so all her measurements will coincide with his measurements.
There remains the case when (max - min) = 2. Each Anya measurement should be at least min and not more than max. We need to brute how many of minimal measurements equal to min Anya will write down from 0 to n. Then the numbers of measurements equal to (min + 1) and max can be uniquely determined.
Let sum is the necessary sum of all measurements, which is equal to the sum of all Kirill measurements, and cntMin is the current number of minimal measurements that Anya will write down. Then Anya needs to write remaining number of measurements such that their sum equals to leftSum = sum - cntMin cdotmin.
The minimum sum that Anya can get with the remaining measurements is minSum = (n - cntMin) cdot(min + 1), and the maximum is maxSum = (n - cntMin) cdotmax. Then, if leftSum < minSum or leftSum > maxSum, Anya can not take cntMin minimum values ​​and get the desired sum.
Otherwise, Anya should write the measurements equal to (min + 1) in the amount of (leftSum - minSum), and all remaining measurements will be equal to the max. After that, we need to update the answer with the number of coinciding values ​​of min, (min + 1) and max in Anya's and Kirill's measurements.
After we updated the answer, move to the next value cntMin.