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.

Example

344

3

题意：问一个数最少分成的平方和个数。

题解：dp[0]=0,dp[1]=1,dp[2]=2,dp[3]=3,dp[4]=1;

接着dp[i]=min(dp[i],dp[i-j*j]+1),这里j从1到sqrt（i）遍历取最小值。

接下来可以看到1，2，3，4也符合递推式。

#include<bits/stdc++.h>
using namespace std;
const int INF=0x3f3f3f3f;
int dp[60060];
int main()
{
    int n;
    cin>>n;
    memset(dp,INF,sizeof(dp));
    dp[0]=0;
    for(int i=1; i<=n; i++)
    {
        int x=sqrt(i);
        for(int j=1; j<=x; j++)
        {
            dp[i]=min(dp[i],dp[i-j*j]+1);
        }
    }
    cout<<dp[n]<<endl;
    return 0;
}