Pink and Blue

Pink and Blue Xenny was a teacher and he had N students. The N children were sitting in a room. Each child 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 Xenny. This made the students very happy. Xenny 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, Xenny 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, Xenny 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. Input The first line is the number of test cases T. First line of each test case 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. Output If Xenny could distribute the T-Shirts in the desired way, print the minimum number of inversions required. Else, print -1. Constraints 1 ≤ N ≤ 105 1 ≤ M ≤ 105 1 ≤ u, v ≤ N Colors of T-Shirt are represented by uppercase characters 'B' and 'G' Sample Input 3 3 2 B G B 1 2 1 3 6 9 B B B G G G 3 5 2 6 4 2 6 3 3 1 3 4 6 1 5 1 1 4 6 5 G G G B G G 6 3 1 3 2 3 4 3 5 3 Output 1 -1 2 Explanation #1 Student 1 can be given a Blue T-Shirt. Hence, Student 2 and 3 would receive Pink T-Shirts. Since, Student 3 is a Boy and has received a Pink T-Shirt, number of inversions = 1.