Square Country

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 a2 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

inputoutput

344

3

/**就是求一个数最少等于几个平方数的和~~~不知道定理的人一般就当背包做了，那样一定超时= =！   ~~~~~四平方和定理~~~~~见链接：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 61006int value(int n)/**四平方和定理(因为在dp分组里找到了这道题,所以自然认为是dp题,不该啊~~~~)**/{    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;}