PAT乙级 1003我要通过！python

PS：这道题是人类迷惑行为……

这是乙级中的第3题，但我做的时候跟第5题似的卡了一下，对逻辑的严密性是一种考验。

n = int(input())
for i in range(n):
    idx = 0;a = 0;b = 0;c = 0;flag = 0
    str = input()
    if 'P' in str and 'A' in str and 'T' in str:
        loc1 = str.index('P')
        loc2 = str.index('T')
        for i in range(loc1):
            if str[i] != 'A':
                flag = 1
            else:
                a += 1
        for i in range(loc1+1,loc2):
            if str[i] != 'A':
                flag = 1
            else:
                b += 1
        for i in range(loc2+1,len(str)):
            if str[i] != 'A':
                flag = 1
            else:
                c += 1
        if flag == 0 and c == a*b :
            print('YES')
        else:
            print('NO')
    else:
        print('NO')