Tkinter how to have separate functions for right and left click on a grid of buttons

Question

class main:
def __init__(self, master, grid=grid):
    frame = tk.Frame(master)
    frame.pack()
    self.grid = grid
    self.buttons = [[None for _ in range(size)] for _ in range(size)]

    for i in range(size):
        for j in range(size):
            self.buttons[i][j] = tk.Button(frame, text=" ", 
                    height='1', width='3')#,
                    # command=lambda i=i, j=j: self.search(i, j))
            self.buttons[i][j].grid(row=i, column=j)
    for i in range(size):
        for j in range(size): 
            self.buttons[i][j].bind("<Button-1>", self.search(i,j))
            self.buttons[i][j].bind("<Button-3>", print('a'))

Above is code where I try to add separate functions for right and left click with a grid of buttons in tkinter, any input on how I can do this?