Square Country

Time limit: 1.0 second

Memory limit: 64 MB

There live square people in a square country. Everything in this country is square also. Thus, the Square Parliament has passed a law about a land. According to the law each citizen of the country has a right to buy land. A land is sold in squares, surely. Moreover, a length of a square side must be a positive integer amount of meters. Buying a square of land with a side  a one pays  a 2 quadrics (a local currency) and gets a square certificate of a landowner. One citizen of the country has decided to invest all of his  N quadrics into the land. He can, surely, do it, buying square pieces 1 × 1 meters. At the same time the citizen has requested to minimize an amount of pieces he buys: "It will be easier for me to pay taxes," — he has said. He has bought the land successfully. Your task is to find out a number of certificates he has gotten.

Input

The only line contains a positive integer  N ≤ 60 000 , that is a number of quadrics that the citizen has invested.

Output

The only line contains a number of certificates that he has gotten.

Sample

input	output
344	3

/**
就是求一個數最少等于幾個平方數的和~~~不知道定理的人一般就當背包做了，那樣一定逾時= =！
   ~~~~~四平方和定理~~~~~
見連結：
http://zh.wikipedia.org/wiki/%E5%9B%9B%E5%B9%B3%E6%96%B9%E5%92%8C%E5%AE%9A%E7%90%86
**/
#include<iostream>
#include<cmath>
#include<cstdio>

using namespace std;
#define maxn 61006

int value(int n)/**四平方和定理(因為在dp分組裡找到了這道題,是以自然認為是dp題,不該啊~~~~)**/
{
    int i,j,k;
    int data;
    if(n==1)
        return 1;
    data=sqrt(n);
    for(i=0; i<=data; i++)
        if(n==i*i)
            return 1;
    for(i=0; i<=data; i++)
        for(j=i; j<=data; j++)
            if(n==i*i+j*j)
                return 2;
    for(i=0; i<=data; i++)
        for(j=i; j<=data; j++)
            for(k=j; k<=data; k++)
                if(n==i*i+j*j+k*k)
                    return 3;
    return 4;
}
void read()
{
    int n;
    scanf("%d",&n);
    printf("%d\n",value(n));
}

int main()
{
    read();
    return 0;
}