Dr. Viru Sahastrabuddhe was a strict professor and he had N students. The N student were sitting in a room. Each student was wearing a white T-shirt, with a unique number from the range 1 to N written on it. T-Shirts of pink and blue color were to be distributed among the students by Dr. Viru Sahastrabuddhe. This made the students very happy. Dr. Viru Sahastrabuddhe felt that a random distribution of T-Shirts would be very uninteresting.
So, he decided to keep an interesting condition:
Every student would get a T-Shirt that is of a different color than his/her friends. That is, if X and Y are friends and X has a Pink T-Shirt, then Y should compulsorily have a Blue T-Shirt, and vice-versa. Also, Dr. Viru Sahastrabuddhe had a belief that Boys should wear blue T-Shirts and Girls should wear pink T-Shirts. If a boy was given a pink T-Shirt or a girl was given a Blue T-Shirt, he called it an inversion. So, Dr. Viru Sahastrabuddhe wanted to distribute T-Shirts in the above-mentioned interesting manner and also wanted to minimize “inversions”. Help him solve the task.
Note: There are no disjoint groups of friends in the room. That is, 2 distinct groups with finite number of students do not exist, but exactly 1 group of students exists in the given situation.
1 ≤ N ≤ 10^5
1 ≤ M ≤ 10^5
1 ≤ u, v ≤ N
Colours of T-Shirt are represented by uppercase characters ‘B’ and ‘G’
First line contains 2 space-separated integers - N and M - number of students and number of friendships present respectively.
Second line consists of N space-separated characters, where ith character denotes the gender of the ith student. B: Boy, G: Girl.
M lines follow. Each line consists of 2 space-separated integers, u and v, showing that u is a friend of v and vice-versa.
If Dr. Viru Sahastrabuddhe could distribute the T-Shirts in the desired way, print the minimum number of inversions required.
Else, print “Not possible”.
Logical Test-Case 1 →
B B G B G G B G