# balance_detect_2.py

# balance_detect_2.py

import random
from itertools import permutations


brackets = permutations(['(','X',')']*3)
brackets = list(set(brackets))
random.shuffle(brackets)
balance_count = 0

for i in brackets:
    balance_check = 0
    sss = ''.join(i)
    p = ''
    for s in sss:
        if s == '(':
            balance_check += 1
        elif s == ')':
            balance_check -= 1
            if balance_check < 0:
                break
        else:
            if p == 'X':
                balance_check = -1
                break
        p = s
    balance_check = 'no' if balance_check else 'yes'
    if balance_check == 'yes': balance_count += 1
    print(sss + ' ' + balance_check)

print(str(balance_count) + ' ' + str(len(brackets)))