Two players, S and T, are playing a game where they make alternate moves. S plays
first.

In this game, they start with an integer N. In each move, a player removes one digit from the integer and passes the resulting number to the other player. The game continues in this fashion until a player finds he/she has no digit
to remove when that player is declared as the loser.

With this restriction, it’s obvious that if the number of digits in N is odd then S wins
otherwise T wins. To make the game more interesting, we apply one additional constraint. A player can remove a particular digit if the sum of digits of the resulting number is a multiple of 3 or there are no digits
left.

Suppose N = 1234. S has 4 possible moves. That is, he can remove 1, 2, 3, or 4.  Of
these, two of them are valid moves.

- Removal of 4 results in 123 and the sum of digits = 1 + 2 + 3 = 6; 6 is a multiple of 3.

- Removal of 1 results in 234 and the sum of digits = 2 + 3 + 4 = 9; 9 is a multiple of 3.

The other two moves are invalid.

If both players play perfectly, who wins?

Input

The first line of input is an integer T(T<60) that determines the number of test cases.
Each case is a line that contains a positive integer N. N has at most 1000 digits and does not contain any zeros.

Output

For each case, output the case number starting from 1. If S wins
then output ‘S’ otherwise output ‘T’.

Sample Input                             Output
for Sample Input

题目大意：两个人博弈，轮流从一列数字里取数，要求剩下的数字之和必须是3的倍数，或者为空。不满足条件者输。

比较简单的博弈，两种情况，一种情况只有一个数字，后手输。第二种情况又分两种情况，第一种是先手可以取数，那么取完之后，接下来的人必取3的倍数，只要统计出三的倍数有多少个就ok了。

#include<stdio.h>
#include<string.h>
char a[1005];
int b[1005];
int main() {
    int t;
    scanf("%d%*c",&t);
    for(int ca=1;ca<=t;ca++) {
        scanf("%s",a);
        printf("Case %d: ",ca);
        int n=strlen(a);
        if(n == 1) {
            printf("S\n");
            continue;
        }
        int cnt=0 , sum=0 ,cnt2=0;
        for(int i=0;i<n;i++) {
            b[i]=a[i]-'0';
            sum+=b[i];
            if(a[i] == '3' || a[i] == '6' || a[i] == '9' ) {
                cnt++;
            } else {cnt2++;}
        }
        if(sum%3 == 0) {
            if(cnt%2 == 1) printf("S\n");
            else printf("T\n");
        } else {
            int i;
            for(i=0;i<n;i++) {
                if((sum-b[i])%3 == 0 ) {
                    break;

                }
            }
            if( i == n ) {printf("T\n");continue;}
            if(cnt%2 == 1) printf("T\n");
            else printf("S\n");
        }
    }
    return 0;
}



Uva 11489 - Integer Game