There are colorful flowers in the parterre in front of the door of college and form many beautiful patterns. Now, you want to find a circle consist of flowers with same color. What should be done ?
Assuming the flowers arranged as matrix in parterre, indicated by a N*M matrix. Every point in the matrix indicates the color of a flower. We use the same uppercase letter to represent the same kind of color. We think a sequence of points d1, d2, … dk makes up a circle while:
1. Every point is different.
2. k >= 4
3. All points belong to the same color.
4. For 1 <= i <= k-1, di is adjacent to di+1 and dk is adjacent to d1. ( Point x is adjacent to Point y while they have the common edge).
N, M <= 50. Judge if there is a circle in the given matrix.