Ural 1465. Pawn Game nim博弈

1465. Pawn Game

Time limit: 1.0 second
Memory limit: 64 MB

In their free time, Santa Claus Petrovich and Santa Claus Egorych play the following game. Pawns are arranged on a board 3×3 in the following way:

Pawns move and attack according to the standard chess rules, and there is one additional rule: it is obligatory to attack. The one who cannot make a move loses. White moves first. For the last 100 years, Petrovich have been playing white and he always won. Once Egorych became tired of this and brought a board 3×5. But he again was losing constantly playing black. "What's the matter", he thought and decided to buy a board 3×N:

And here Petrovich has to think which color to play in order to win. Help him to decide.

Input

The integer N (1 ≤ N ≤ 109).

Output

"White" if Petrovich should play white, and "Black" if he should play black. Egorych and Petrovich always make moves according to their optimal strategies.

Samples

inputoutput

3

White

4

Black

5

White

Problem Author: Alexander Toropov
Problem Source: Ural SU Contest. Petrozavodsk Winter Session, January 2006

//nim博弈#include <iostream>using namespace std;int sg[100000];int a[10000];int b[1000]= {1,0,0,0,0,0,1,0,0,0,1};string m[2]= {"White","Black"};int c[10000];int main(){    sg[1]=1;    sg[2]=1;    int cnt=0;    for(int i=3; i<=5000; i++)    {        a[sg[i-2]]=i;        for(int j=0; j<=i-3; j++)            a[(sg[j]^sg[i-j-3])]=i;        for(int j=0; j<=i; j++)            if(a[j]!=i)            {                sg[i]=j;                break;            }        if(i>82)        {            c[cnt++]=sg[i];        }    }    int n;    cin>>n;    if(n<=82)    {        if(sg[n])            cout<<"White"<<endl;        else            cout<<"Black"<<endl;    }    else    {        n-=83;        if(c[n%34])            cout<<"White"<<endl;        else            cout<<"Black"<<endl;    }}