C. Laboratory Work

time limit per test : 1 second

memory limit per test : 256 megabytes

input : standard input

output : standard output

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: \(x_1, x_2, ..., x_n\). 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 \(y_1, y_2, ..., y_n\) in her work, that the following conditions are met:

  • the average value of \(x_1, x_2, ..., x_n\) is equal to the average value of \(y_1, y_2, ..., y_n\);

    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

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 \(x_1, x_2, ..., x_n ( - 100 000 ≤ x_i ≤ 100 000)\) — the measurements made by Kirill. It is guaranteed that the difference between the maximum and minimum values among values \(x_1, x_2, ..., x_n\) does not exceed \(2\).

Output

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

In the second line print n integers \(y_1, y_2, ..., y_n\) — 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.

Examples

input

6

-1 1 1 0 0 -1

output

2

0 0 0 0 0 0

input

3

100 100 101

output

3

101 100 100

input

7

-10 -9 -10 -8 -10 -9 -9

output

5

-10 -10 -9 -9 -9 -9 -9

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 \(5\).

题意

给出一个数组\(a\),要求构造一个新的数组\(b\),满足:

  1. \(b\)数组的平均值和\(a\)数组的平均值相等,
  2. \(b\)数组的最大值不大于\(a\)数组的最大值,最小值不小于\(a\)数组的最小值
  3. 要求\(a,b\)数组不同的元素尽可能多

思路

因为题目中给出了:数组中最大值和最小值的差值不超过\(2\),可以分成两种情况:

  1. 当\(a\)数组中的最大值和最小值差值小于\(2\)的时候,无法构造出一个和\(a\)不同的满足条件的\(b\)数组,相同元素个数为\(n\)
  2. 当最大值和最小值差值等于\(2\)时,可以将\(a\)数组转换成只有\(0,1,2\)的一个新数组,然后有两种方案进行构造:
  • 方案一:将两个\(1\)变成一个\(0\)和一个\(2\)
  • 方案二:将一个\(0\)和一个\(2\)变成两个\(1\)

当\(1\)较少的时候,选择方案二,当\(1\)比\(2\)和\(0\)的个数多的时候,选择方案一

代码

#include <bits/stdc++.h>
#define ll long long
#define ull unsigned long long
#define ms(a,b) memset(a,b,sizeof(a))
const int inf=0x3f3f3f3f;
const ll INF=0x3f3f3f3f3f3f3f3f;
const int maxn=1e6+10;
const int mod=1e9+7;
const int maxm=1e3+10;
using namespace std;
int a[maxn];
int num[maxn];
bool cmp(int a,int b)
{
return a>b;
}
int main(int argc, char const *argv[])
{
#ifndef ONLINE_JUDGE
freopen("in.txt", "r", stdin);
freopen("out.txt", "w", stdout);
srand((unsigned int)time(NULL));
#endif
ios::sync_with_stdio(false);
cin.tie(0);
int n;
cin>>n;
int minn=inf;
int maxx=-inf;
for(int i=0;i<n;i++)
{
cin>>a[i];
minn=min(a[i],minn);
maxx=max(maxx,a[i]);
}
if(maxx-minn<=1)
{
cout<<n<<endl;
sort(a,a+n,cmp);
for(int i=0;i<n;i++)
cout<<a[i]<<" ";
cout<<endl;
}
else
{
for(int i=0;i<n;i++)
a[i]-=minn,num[a[i]]++;
// 两个1变成一个0和一个2
// 一个0和一个2变成两个1
int res=min(num[0],num[2]);
int res1=num[1]/2;
// 如果1比较少,选择方案二
if(res>res1)
{
num[1]+=res*2;
num[0]-=res;
num[2]-=res;
}
// 如果1比较多,选择方案一
else
{
res=res1;
num[1]-=res*2;
num[0]+=res;
num[2]+=res;
}
cout<<n-res*2<<endl;
for(int i=0;i<3;i++)
for(int j=0;j<num[i];j++)
cout<<minn+i<<" ";
cout<<endl;
}
#ifndef ONLINE_JUDGE
cerr<<"Time elapsed: "<<1.0*clock()/CLOCKS_PER_SEC<<" s.\n";
#endif
return 0;
}

Codeforces 931C:Laboratory Work(构造)的更多相关文章

  1. CodeForces 931C Laboratory Work 水题,构造

    *这种题好像不用写题解... 题意: 一个人要改动别人的实验记录,实验记录记录是一个集合 实验记录本身满足:$max(X)-min(X)<=2$ 改动结果要求: 1.新的集合平均值和之前的一样 ...

  2. Codeforces 1383D - Rearrange(构造)

    Codeforces 题面传送门 & 洛谷题面传送门 一道不算困难的构造,花了一节英语课把它搞出来了,题解简单写写吧( 考虑从大往小加数,显然第三个条件可以被翻译为,每次加入一个元素,如果它所 ...

  3. Codeforces 549B. Looksery Party[构造]

    B. Looksery Party time limit per test 1 second memory limit per test 256 megabytes input standard in ...

  4. codeforces 323A. Black-and-White Cube 构造

    输入n 1 <= n <= 100 有一个n * n * n 的立方体,由n ^ 3 个1 * 1 * 1 的单位立方体构成 要用white 和 black 2种颜色来染这n ^ 3个立方 ...

  5. Codeforces Gym 100531I Instruction 构造

    Problem I. Instruction 题目连接: http://codeforces.com/gym/100531/attachments Description Ingrid is a he ...

  6. codeforces 22C System Administrator(构造水题)

    转载请注明出处: http://www.cnblogs.com/fraud/          ——by fraud System Administrator Bob got a job as a s ...

  7. Codeforces 353D Queue(构造法)

    [题目链接] http://codeforces.com/contest/353/problem/D [题目大意] 10^6个男女排队,每一秒,如果男生在女生前面,即pos[i]是男生,pos[i+1 ...

  8. Codeforces 482 - Diverse Permutation 构造题

    这是一道蛮基础的构造题. - k         +(k - 1)      -(k - 2) 1 + k ,    1 ,         k ,             2,    ....... ...

  9. [ An Ac a Day ^_^ ] CodeForces 468A 24 Game 构造

    题意是让你用1到n的数构造24 看完题解感觉被样例骗了…… 很明显 n<4肯定不行 然后构造出来4 5的组成24的式子 把大于4(偶数)或者5(奇数)的数构造成i-(i-1)=1 之后就是无尽的 ...

随机推荐

  1. 13 — springboot集成mybatis-plus — 更新完毕

    1.mybatis-plus需要掌握的知识 1).mybatis-plus是什么? 不写了,老衲一般都是直接进官网 mybatis-plus官网地址:https://baomidou.com/guid ...

  2. absent, absolute

    absent 1. A teacher asked in a class who killed Abraham Lincoln. A blonde said "It wasn't me, I ...

  3. Tomcat中的Server.xml配置详解

    Tomcat中的Server.xml配置详解 Tomcat Server的结构图如下: 该文件描述了如何启动Tomcat Server <Server> <Listener /> ...

  4. Docker学习(五)——Docker仓库管理

    Docker仓库管理     仓库(Repository)是集中存放镜像的地方. 1.Docker Hub       目前Docker官方维护了一个公共仓库Docker Hub.大部分需求都可以通过 ...

  5. Linux学习 - 数值运算

    1 declare 声明变量类型 declare [+/-] [选项] 变量名 - 给变量设定类型属性 + 取消变量的类型属性 -i 将变量声明为整数型 -x 将变量声明为环境变量(同export) ...

  6. [学习总结]7、Android AsyncTask完全解析,带你从源码的角度彻底理解

    我们都知道,Android UI是线程不安全的,如果想要在子线程里进行UI操作,就需要借助Android的异步消息处理机制.之前我也写过了一篇文章从源码层面分析了Android的异步消息处理机制,感兴 ...

  7. 格式化代码(Eclipse 格式化代码块快捷键:Ctrl+Shift+F)

    1.格式化java代码 : ①Ctrl+Shift+F 但是我们会遇到按 Ctrl+Shift+F不起作用的时候?       Ctrl+Shift+F 在搜狗拼音里是简繁替换.一旦安装搜狗拼音这个快 ...

  8. Linux基础命令---lftp登录ftp服务器

    lftp lftp指令可以用来登录远程ftp服务器,这是一个字符界面的文件传输工具. 此命令的适用范围:RedHat.RHEL.Ubuntu.CentOS.SUSE.openSUSE.Fedora. ...

  9. Spring事务隔离级别和传播特性(转)

    相信每个人都被问过无数次Spring声明式事务的隔离级别和传播机制吧!今天我也来说说这两个东西. 加入一个小插曲,一天电话里有人问我声明式事务隔离级别有哪几种,我就回答了7种,他问我Spring的版本 ...

  10. Linux下部署Java项目(jetty作为容器)常用脚本命令

    startup.sh #!/bin/bash echo $(basename $(pwd)) "jetty started" cd jetty nohup java -Xmx8g ...