MasterMind is a game for two players. One of them, Designer, selects a secret code. The other, Breaker, tries to break it. A code is no more than a row of colored dots. At the beginning of a game, the players agree upon the length N that a code must have and upon the colors that may occur in a code.

In order to break the code, Breaker makes a number of guesses, each guess itself being a code. After each guess Designer gives a hint, stating to what extent the guess matches his secret code.

In this problem you will be given a secret code  and a guess  , and are to determine the hint. A hint consists of a pair of numbers determined as follows.

A match is a pair (i,j),  and  , such that  . Match (i,j) is called strong when i = j, and is called weak otherwise. Two matches (i,j) and (p,q) are called independent when i = p if and only if j = q. A set of matches is called independent when all of its members are pairwise independent.

Designer chooses an independent set M of matches for which the total number of matches and the number of strong matches are both maximal. The hint then consists of the number of strong followed by the number of weak matches in M. Note that these numbers are uniquely determined by the secret code and the guess. If the hint turns out to be (n,0), then the guess is identical to the secret code.

The output for each game should list the hints that would be generated for each guess, in order, one hint per line. Each hint should be represented as a pair of integers enclosed in parentheses and separated by a comma. The entire list of hints for each game should be prefixed by a heading indicating the game number; games are numbered sequentially starting with 1. Look at the samples below for the exact format.

4
1 3 5 5
1 1 2 3
4 3 3 5
6 5 5 1
6 1 3 5
1 3 5 5
0 0 0 0
10
1 2 2 2 4 5 6 6 6 9
1 2 3 4 5 6 7 8 9 1
1 1 2 2 3 3 4 4 5 5
1 2 1 3 1 5 1 6 1 9
1 2 2 5 5 5 6 6 6 7
0 0 0 0 0 0 0 0 0 0
0

Game 1:
    (1,1)
    (2,0)
    (1,2)
    (1,2)
    (4,0)
Game 2:
    (2,4)
    (3,2)
    (5,0)
    (7,0)

#include<iostream>
#include<algorithm>
#include<stdio.h>
#include<string.h>
#include<stdlib.h>

using namespace std;

struct node
{
    int x,y;
}q[100010];
int a[10];
int b[100010];
int c[100001];
int aa[10];

int main()
{
    int n;
    int e = 0;
    while(scanf("%d",&n)!=EOF)
    {
        if(n == 0)
        {
            break;
        }
        memset(a,0,sizeof(a));
        for(int i=0;i<n;i++)
        {
            scanf("%d",&b[i]);
            a[b[i]]++;
        }
        int flag = 0;
        int k = 0;
        while(flag!=1)
        {
            memset(aa,0,sizeof(aa));
            for(int i=0;i<=10;i++)
            {
                aa[i] = a[i];
            }
            int count1 = 0;
            int count2 = 0;
            int tt = 0;
            for(int i=0;i<n;i++)
            {
                scanf("%d",&c[i]);
                if(c[i] == 0)
                {
                    tt++;
                    if(tt == n)
                    {
                        flag = 1;
                        break;
                    }
                }
                if(b[i] == c[i])
                {
                    count1++;
                    aa[c[i]]--;
                    c[i] = 10;
                }
            }
            for(int i=0;i<n;i++)
            {
                if(aa[c[i]] >=1)
                {
                    count2++;
                    aa[c[i]]--;
                }
            }
            q[k].x = count1;
            q[k].y = count2;
            k++;
        }
        printf("Game %d:\n",++e);
        for(int i=0;i<k-1;i++)
        {
            printf("    (%d,%d)\n",q[i].x,q[i].y);
        }
    }
    return 0;
}