In Computer Science branch of ABC College of Engineering, there are n students; numbered 0 through n-1(where n is an odd number). As usual, each of the student has some friends within the same branch, and each of them knows how many friends each of the other student has. Friendship is symmetric, so if a student 0 is a friend of student 1, then student 1 is also a friend of student 0. An assignment is given to the students by Prof. XYZ, for which groups of 2 are to be formed within the classroom, for which each student has been asked to submit the name of the student with whom they want to form their assignment group. Each student ‘i’ has got the freedom to choose exactly 1 other student (i+k)%n as his/her partner for the assignment, not necessarily a friend; and each student is free to select anyone. For example, if a student 0 selects student 1 then too student 1 can select any student other than 0 as his group-mate. You being the Prof. XYZ ask each student to submit the "sum of the number of friends each of the student in class have, other than the student himself and the one he chose for the assignment group”. For example, if student 0 selects student 1 for his group, he should submit (the number of friends kid 2 has) + (the number of friends kid 3 has) + ... + (the number of friends kid n-1 has). You are given a vector sumFriends, where the i-th element (0-indexed) is the answer given to you by student i. To make the things complicated for you, some of the students might not be telling the truth. Return "IMPOSSIBLE" if it is impossible for all the given answers to be accurate. Otherwise, return "POSSIBLE".
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