Problem: You are given a string s, consisting only of characters '0' or '1'. Let |s| be the length of s.

You are asked to choose some integer k (k > 0) and find a sequence a of length k such that: 

  * 1 ≤ a_1 < a_2 < ... < a_k ≤ |s|; 
  * a_{i-1} + 1 < a_i for all i from 2 to k. 



The characters at positions a_1, a_2, ..., a_k are removed, the remaining characters are concatenated without changing the order. So, in other words, the positions in the sequence a should not be adjacent.

Let the resulting string be s'. s' is called sorted if for all i from 2 to |s'| s'_{i-1} ≤ s'_i.

Does there exist such a sequence a that the resulting string s' is sorted?

Input

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of testcases.

Then the descriptions of t testcases follow.

The only line of each testcase contains a string s (2 ≤ |s| ≤ 100). Each character is either '0' or '1'.

Output

For each testcase print "YES" if there exists a sequence a such that removing the characters at positions a_1, a_2, ..., a_k and concatenating the parts without changing the order produces a sorted string.

Otherwise, print "NO".

You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES are all recognized as positive answer).

Example

Input


5
10101011011
0000
11111
110
1100


Output


YES
YES
YES
YES
NO

Note

In the first testcase you can choose a sequence a=[1,3,6,9]. Removing the underlined letters from "10101011011" will produce a string "0011111", which is sorted.

In the second and the third testcases the sequences are already sorted.

In the fourth testcase you can choose a sequence a=[3]. s'= "11", which is sorted.

In the fifth testcase there is no way to choose a sequence a such that s' is sorted.

Solution (in PYTHON):

Solution:


from __future__ import division, print_function

import os,sys
from io import BytesIO, IOBase

if sys.version_info[0] < 3:
    from __builtin__ import xrange as range
    from future_builtins import ascii, filter, hex, map, oct, zip


# sys.setrecursionlimit(10000000)


def dmain():
    sys.setrecursionlimit(1000000)
    threading.stack_size(1024000)
    thread = threading.Thread(target=main)
    thread.start()
    
#from collections import deque, Counter, OrderedDict,defaultdict
#from heapq import nsmallest, nlargest, heapify,heappop ,heappush, heapreplace
#from math import log,sqrt,factorial,cos,tan,sin,radians
#from bisect import bisect,bisect_left,bisect_right,insort,insort_left,insort_right
#from decimal import *
#import threading
#from itertools import permutations
#Copy 2D list  m = [x[:] for x in mark] .. Avoid Using Deepcopy

# abc='abcdefghijklmnopqrstuvwxyz'
# abd={'a': 0, 'b': 1, 'c': 2, 'd': 3, 'e': 4, 'f': 5, 'g': 6, 'h': 7, 'i': 8, 'j': 9, 'k': 10, 'l': 11, 'm': 12, 'n': 13, 'o': 14, 'p': 15, 'q': 16, 'r': 17, 's': 18, 't': 19, 'u': 20, 'v': 21, 'w': 22, 'x': 23, 'y': 24, 'z': 25}
# mod=1000000007
# #mod=998244353
# inf = float("inf")
# vow=['a','e','i','o','u']
# dx,dy=[-1,1,0,0],[0,0,1,-1]
# def getKey(item): return item[1] 
# def sort2(l):return sorted(l, key=getKey,reverse=True)
# def d2(n,m,num):return [[num for x in range(m)] for y in range(n)]
# def isPowerOfTwo (x): return (x and (not(x & (x - 1))) )
# def decimalToBinary(n): return bin(n).replace("0b","")
# def ntl(n):return [int(i) for i in str(n)]
# def ncr(n,r): return factorial(n)//(factorial(r)*factorial(max(n-r,1)))

# def ceil(x,y):
#     if x%y==0:
#         return x//y
#     else:
#         return x//y+1

# def powerMod(x,y,p):
#     res = 1
#     x %= p
#     while y > 0:
#         if y&1:
#             res = (res*x)%p
#         y = y>>1
#         x = (x*x)%p
#     return res

# def gcd(x, y):
#     while y:
#         x, y = y, x % y
#     return x
    
def isPrime(n) : # Check Prime Number or not 
    if (n <= 1) : return False
    if (n <= 3) : return True
    if (n % 2 == 0 or n % 3 == 0) : return False
    i = 5
    while(i * i <= n) : 
        if (n % i == 0 or n % (i + 2) == 0) : 
            return False
        i = i + 6
    return True

def lower_bound(l,k):
    s = 0
    e = len(l)
    while(s<e):
        m = (s+e-1)//2
        if(l[m] <= k):
            s = m+1
        else:
            e = m
    return s

def upper_bound(l,k):
    s = 0
    e = len(l)
    while(s<e):
        m = (s+e-1)//2
        if(l[m] >= k):
            e = m
        else:
            s = m+1
    return s

def bs(l,k):
    s = 0
    e = len(l) - 1
    while(s<=e):
        m = (s+e)//2
        if(l[m] == k):
            return m
        elif(l[m] > k):
            e = m-1
        else:
            s = m+1
    return -1


# l = [0]*1000001
# v = [0]*1000001
# d = [0]*1000001
# from queue import Queue
def bfs(n):
    v[n] = 1
    q = Queue()
    q.put(n)
    d[n] = 0
    while(not q.empty()):
        cur = q.get()
        # print(cur,v[:5],q)
        for i in l[cur]:
            if(v[i]==0):
                v[i] = 1
                d[i] = d[cur] + 1
                q.put(i)

def valid(a,b):
    c = 0
    while(a>0):
        if(a%10 == b%10):
            c += 1
        a = a//10
        b = b//10
    if(c==3):
        return True
    return False

col = [0]*1000001
def dfs(n,c):
    v[n] = 1
    col[n] = c
    for i in l[n]:
        if(v[i]==0):
            dfs(i, c)



def read():
    sys.stdin  = open('input.txt', 'r')  
    sys.stdout = open('output.txt', 'w') 


def ii():  return int(input())
def si():  return input()
def mi():  return map(int,input().strip().split(" "))
def msi(): return map(str,input().strip().split(" "))
def li():  return list(mi())


def main():
    # read()

    for _ in range(ii()):
        s = si()
        f = 1
        f0 = 0
        f1 = 0
        n = len(s)
        for i in range(1,n):
            if(s[i]==s[i-1] and s[i]=='0' and f1):
                f = 0
                break
            if(s[i]==s[i-1] and s[i]=='1'):
                f1 = 1
        if(f):
            print("YES")
        else:
            print("NO")










# region fastio
# template taken from https://github.com/cheran-senthil/PyRival/blob/master/templates/template.py

BUFSIZE = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


def print(*args, **kwargs):
    """Prints the values to a stream, or to sys.stdout by default."""
    sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout)
    at_start = True
    for x in args:
        if not at_start:
            file.write(sep)
        file.write(str(x))
        at_start = False
    file.write(kwargs.pop("end", "\n"))
    if kwargs.pop("flush", False):
        file.flush()


if sys.version_info[0] < 3:
    sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout)
else:
    sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)

input = lambda: sys.stdin.readline().rstrip("\r\n")

# endregion


if __name__ == "__main__":
    
    main()
    # dmain()

# Comment Read()