Mrs. Smith is trying to contact her husband, John Smith, but she forgot the secret phone number!
The only thing Mrs. Smith remembered was that any permutation of nn can be a secret phone number. Only those permutations that minimize secret value might be the phone of her husband.
The sequence of nn integers is called a permutation if it contains all integers from 11 to nn exactly once.
The secret value of a phone number is defined as the sum of the length of the longest increasing subsequence (LIS) and length of the longest decreasing subsequence (LDS).
A subsequence ai1,ai2,…,aikai1,ai2,…,aik where 1≤i1<i2<…<ik≤n1≤i1<i2<…<ik≤n is called increasing if ai1<ai2<ai3<…<aikai1<ai2<ai3<…<aik . If ai1>ai2>ai3>…>aikai1>ai2>ai3>…>aik , a subsequence is called decreasing. An increasing/decreasing subsequence is called longest if it has maximum length among all increasing/decreasing subsequences.
For example, if there is a permutation [6,4,1,7,2,3,5][6,4,1,7,2,3,5] , LIS of this permutation will be [1,2,3,5][1,2,3,5] , so the length of LIS is equal to 44 . LDS can be [6,4,1][6,4,1] , [6,4,2][6,4,2] , or [6,4,3][6,4,3] , so the length of LDS is 33 .
Note, the lengths of LIS and LDS can be different.
So please help Mrs. Smith to find a permutation that gives a minimum sum of lengths of LIS and LDS.
Input
The only line contains one integer nn (1≤n≤1051≤n≤105 ) — the length of permutation that you need to build.
Output
Print a permutation that gives a minimum sum of lengths of LIS and LDS.
If there are multiple answers, print any.
Examples
Input
4
Output
3 4 1 2
Input
2
Output
2 1
Note
In the first sample, you can build a permutation [3,4,1,2][3,4,1,2] . LIS is [3,4][3,4] (or [1,2][1,2] ), so the length of LIS is equal to 22 . LDS can be ony of [3,1][3,1] , [4,2][4,2] , [3,2][3,2] , or [4,1][4,1] . The length of LDS is also equal to 22 . The sum is equal to 44 . Note that [3,4,1,2][3,4,1,2] is not the only permutation that is valid.
In the second sample, you can build a permutation [2,1][2,1] . LIS is [1][1] (or [2][2] ), so the length of LIS is equal to 11 . LDS is [2,1][2,1] , so the length of LDS is equal to 22 . The sum is equal to 33 . Note that permutation [1,2][1,2] is also valid.
分析:
首先是对题意的理解,让我们求一段数字的最长上升和最长下降长度总和。但本题和最长上升子序列应用没半点关系。
具体怎末求呢,我们可以采用分块的方法,将长度为n的序列分为m段。将m段按上升序列排序。则最长上升子序列和最长下降子序列之和。最长上升子序列长度,最长下降m。所以总长度m+所以我们应分为块
AC代码:
#include<iostream>
#include<cstdio>
#include<algorithm>
#include<string.h>
#include<math.h>
using namespace std;
int main()
{
int n;
while(cin >> n)
{
int a = sqrt(n);//分a块
int temp = n, m = n / a;
for (int i = 0; i < m; i++)
{
temp -= a;
for (int j = temp + 1; j <= temp + a; j++)
{
cout << j << " ";
}
}
for (int i = 1; i <= temp; i++)
{
cout << i << " ";
}
cout << endl;
}
return 0;
}