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As the new term comes, the Ignatius Train Station is very busy nowadays. A lot of student want to get back to school by train(because the trains in the Ignatius Train Station is the fastest all over the world ^v^). But here comes a problem, there is only one railway where all the trains stop. So all the trains come in from one side and get out from the other side. For this problem, if train A gets into the railway first, and then train B gets into the railway before train A leaves, train A can't leave until train B leaves. The pictures below figure out the problem. Now the problem for you is, there are at most 9 trains in the station, all the trains has an ID(numbered from 1 to n), the trains get into the railway in an order O1, your task is to determine whether the trains can get out in an order O2. 
  

Input

The input contains several test cases. Each test case consists of an integer, the number of trains, and two strings, the order of the trains come in:O1, and the order of the trains leave:O2. The input is terminated by the end of file. More details in the Sample Input. 

Output

The output contains a string "No." if you can't exchange O2 to O1, or you should output a line contains "Yes.", and then output your way in exchanging the order(you should output "in" for a train getting into the railway, and "out" for a train getting out of the railway). Print a line contains "FINISH" after each test case. More details in the Sample Output. 

Sample Input

3 123 3213 123 312

Sample Output

Yes.inininoutoutoutFINISHNo.FINISH          For the first Sample Input, we let train 1 get in, then train 2 and train 3.So now train 3 is at the top of the railway, so train 3 can leave first, then train 2 and train 1.In the second Sample input, we should let train 3 leave first, so we have to let train 1 get in, then train 2 and train 3.Now we can let train 3 leave.But after that we can't let train 1 leave before train 2, because train 2 is at the top of the railway at the moment.So we output "No.".

Hint

Hint

分析：

要读懂题意,如：1234    1324 是正确的，先进1再出1，接着2 3进3 2出，最后4进4 出。搞明白后就简单多了；

1.如果待入栈火车和最顶目标火车相同就进行连续进栈出栈；

2.若是不相同则只是进栈就行；

3.最后利用出栈次数是否与进栈次数相同进行输出答案；

一定要想清楚了；附答案图一张，方便理解；

代码：

#include<stdio.h>#include<string.h>#include<stack>using namespace std;int main(){    int n, i, j, k, flag[50];//1表示进0表示出;j表示出栈次数；     char s1[15], s2[15];    stack <char> s;    while(~scanf("%d %s%s",&n,s1,s2))    {           while(!s.empty())  s.pop();        memset(flag,-1,sizeof(flag));        j = k = 0;        for(i = 0; i < n; i++)        {            s.push(s1[i]);            flag[k++] = 1;            while(!s.empty() && s.top() == s2[j])            {                flag[k++] = 0;                s.pop();                j++;            }        }        if(j == n)        {            printf("Yes.\n");            for(i = 0; i < k; i++)            {                if(flag[i])                    printf("in\n");                else                    printf("out\n");            }        }        else            printf("No.\n");        printf("FINISH\n");    }    return 0;}