Sample Input 1

7
1 1
1 7
2 8
4 7
7 4
8 2
7 1
15
A 1 3
A 1 4
A 1 5
A 1 6
? 1 3
R 1 3
A 2 4
R 1 6
A 5 7
? 2 5
R 1 5
R 1 4
A 4 7
A 2 7
? 7 4
0

Sample Output 1

24.0
0.0
3.0

Sample Input 1

1
5 13
0 1 1 1 1 1 1 1 0 1 1 1 1
0 1 1 1 1 1 1 1 1 0 1 1 1
0 1 1 1 1 1 1 1 0 0 1 1 1
0 1 1 1 1 1 1 1 0 0 1 1 1
1 1 0 1 1 1 1 1 0 0 1 1 1

Sample Output 1

YES

Sample Input 1

1
6
0 1
-1 0
-1 -1
2 1
2 0
1 -1

Sample Output 1

YES
2
0 0 2
1 0 2

Sample Input 1

2
1 2
1
4 2
7 7 6 6

Sample Output 1

Bash
Chikapu

Sample Input 1

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

Sample Output 1

YES
NO
YES

Sample Input 1

3
hanoi
ionah
ac
wa
hue
hue

Sample Output 1

YES
NO
YES

Sample Input 1

2
1 2 3 4
0

Sample Output 1

2 1 4 3
3 4 1 2

Sample Input 1

3
3
UF
3
VH
4
/zO

Sample Output 1

YES
1 3 2 1
NO
YES
4 2 3 1

Sample Input 1

5 2
2 4 3 1 5

Sample Output 1

2

Sample Input 2

6 120
1 2 3 4 5 6

Sample Output 2

720

Sample Input 3

6 120
1 2 3 4 6 5

Sample Output 3

0

Sample Input 4

10 15
4 8 5 1 3 10 9 2 7 6

Sample Output 4

465

Sample Input 1

2
2 3
1 2
2
1 1
1 0
2
2 2
0 1
3
4 4
0 0
4 4
0

Sample Output 1

2 1 
1 2 
2 1 
1 3 2 

Sample Input 1

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

Sample Output 1

6
0
3
-1

Sample Input 1

2
3
100
3
111

Sample Output 1

NO
YES

Sample Input 1

3
4 9 9
7 5 1 5
6 10 10
1 1 1 1 1 1
7 405 6
103 1 102 2 101 3 100

Sample Output 1

Haros
Iwys
Iwys