8VC Venture Cup 2016 -- Elimination Round Tutorial 626B

Catherine has a deck of n cards, each of which is either red, green, or blue. As long as there are at least two cards left, she can do one of two actions:

take any two (not necessarily adjacent) cards with different colors and exchange them for a new card of the third color;
take any two (not necessarily adjacent) cards with the same color and exchange them for a new card with that color.

She repeats this process until there is only one card left. What are the possible colors for the final card?

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 200) — the total number of cards.

The next line contains a string s of length n — the colors of the cards. s contains only the characters 'B', 'G', and 'R', representing blue, green, and red, respectively.

Output

Print a single string of up to three characters — the possible colors of the final card (using the same symbols as the input) in alphabetical order.

Examples

input

2
RB

output

input

3
GRG

output

BR

input

5
BBBBB

output

Note

In the first sample, Catherine has one red card and one blue card, which she must exchange for a green card.

In the second sample, Catherine has two green cards and one red card. She has two options: she can exchange the two green cards for a green card, then exchange the new green card and the red card for a blue card. Alternatively, she can exchange a green and a red card for a blue card, then exchange the blue card and remaining green card for a red card.

In the third sample, Catherine only has blue cards, so she can only exchange them for more blue cards.

两种同色合成一张该颜色，两种不同色合成另外一种颜色。

感觉还是这个隐式图搜索更有说服力一点。

#include <cstdio>
#include <cstring>
#define M 222 
int jb, jg, jr;
char str[M]; int v[M][M][M];
void dfs(int lb, int lg, int lr)
{
    if(lb==0&&lg==0&&lr==1)
    {
        //if(jr==0)
            jr=1;
        return;
    }
    else if(lb==0&&lg==1&&lr==0)
    {
        //if(jg==0)
            jg=1;
        return;
    }
    else if(lb==1&&lg==0&&lr==0)
    {
        //if(jb==0)
            jb=1;
        return;
    }
    if(lb>0&&lg>0&&!v[lb-1][lg-1][lr+1])
    {
        v[lb-1][lg-1][lr+1]=1;
        dfs(lb-1, lg-1, lr+1);
    }
    if(lb>0&&lr>0&&!v[lb-1][lg+1][lr-1])
    {
        v[lb-1][lg+1][lr-1]=1;
        dfs(lb-1, lg+1, lr-1);
    }
    if(lg>0&&lr>0&&!v[lb+1][lg-1][lr-1])
    {
        v[lb+1][lg-1][lr-1]=1;
        dfs(lb+1,lg-1,lr-1);
    }
    if(lb>1&&!v[lb-1][lg][lr])
    {
        v[lb-1][lg][lr]=1;
        dfs(lb-1, lg, lr);
    }
    if(lg>1&&!v[lb][lg-1][lr])
    {
        v[lb][lg-1][lr]=1;
        dfs(lb, lg-1, lr);
    }    
    if(lr>1&&!v[lb][lg][lr-1])
    {
        v[lb][lg][lr-1]=1;
        dfs(lb, lg, lr-1);
    }    
}
int main()
{
    int n; 
    while(scanf("%d", &n)!=EOF)
    {
        scanf("%s", str);
        int len=strlen(str);
        int lb=0, lg=0, lr=0;
        jb=jg=jr=0;
        for(int i=0; i<len; i++)
        {
            if(str[i]=='B')
                lb++;
            if(str[i]=='G')
                lg++;
            if(str[i]=='R')
                lr++;
        }
    //    printf("%d %d %d
", lb, lg, lr); 
        memset(v, 0, sizeof(v));
        dfs(lb, lg, lr);
        if(jb)
            printf("B"); 
        if(jg)
            printf("G"); 
        if(jr)
            printf("R");
        printf("
");
    }
    return 0;
}