Problem: You are given a binary string s consisting of n zeros and ones.

Your task is to divide the given string into the minimum number of subsequences in such a way that each character of the string belongs to exactly one subsequence and each subsequence looks like "010101 ..." or "101010 ..." (i.e. the subsequence should not contain two adjacent zeros or ones).

Recall that a subsequence is a sequence that can be derived from the given sequence by deleting zero or more elements without changing the order of the remaining elements. For example, subsequences of "1011101" are "0", "1", "11111", "0111", "101", "1001", but not "000", "101010" and "11100".

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow.

The first line of the test case contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of s. The second line of the test case contains n characters '0' and '1' — the string s.

It is guaranteed that the sum of n does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5).

Output

For each test case, print the answer: in the first line print one integer k (1 ≤ k ≤ n) — the minimum number of subsequences you can divide the string s to. In the second line print n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ k), where a_i is the number of subsequence the i-th character of s belongs to.

If there are several answers, you can print any.

Example

Input


4
4
0011
6
111111
5
10101
8
01010000


Output


2
1 2 2 1 
6
1 2 3 4 5 6 
1
1 1 1 1 1 
4
1 1 1 1 1 2 3 4 

Solution (in PYTHON3):

Solution:
import sys, os, io
def rs(): return sys.stdin.readline().rstrip()
def ri(): return int(sys.stdin.readline())
def ria(): return list(map(int, sys.stdin.readline().split()))
def ws(s): sys.stdout.write(s + '\n')
def wi(n): sys.stdout.write(str(n) + '\n')
def wia(a): sys.stdout.write(' '.join([str(x) for x in a]) + '\n')
import math,datetime,functools,itertools,operator,bisect
from collections import deque,defaultdict,OrderedDict
import collections

def main():
    starttime=datetime.datetime.now()
    if(os.path.exists('input.txt')):
        sys.stdin = open("input.txt","r")
        sys.stdout = open("output.txt","w")
    

    for _ in range(ri()):
        n=ri()
        a=rs()
        n0=0
        n1=0
        ns=0
        ans=[]
        p0=[]
        p1=[]
        p=[]
        np=0
        k=[]
        for i in a:
            if i=='0':
                if n1==0:
                    ns+=1
                    n0+=1
                    k.append(ns)
                else:
                    n1-=1
                    n0+=1
                    k.append(n0)
                    
            else:
                if n0==0:
                    ns+=1
                    n1+=1
                    k.append(ns)
                else:
                    k.append(n0)
                    n0-=1
                    n1+=1
                    
                    
        print(ns)
        print(*k)
        
                
        
        
                
                    
        
        
        
        
        
        
        
       
  
            
            

            
                
                
        
        
            
                    
            
            

        
        

    
                
                    
                
                
                
                    
                
        
        
        
        
        
        
        
            
            
        
        
        
            
        
                
        
        
            
            
        
        
                    
                    
        
        

                
                    
        
            
            
                
        
        
           
            
            
            

        
        
        


            
            
            
           
            
            
            
            
        
            
                
            
            
                            
                
            
            
        
            
            
            
            
            
            
        
        
                
                
                
                  
                    
                    
                
            
        
        
                
                
            
        
        
                    
                    
                    
            
            
            
            
            
        

                    
                    
          
        
        
        
            
            
                
                    
            
        
        
                
                    
                    
                    
            

        
            
            

            

                
                
                
                
            
        

        
        
            
            
                
                
        
        
        
                
            
        
        
        
        
        
            
            
        
                
                
                

        

                    
                
            

        
        
            
            
            
                
                
            
                
                
        

                
        
        

        
            
                
                
            
        
            
            
                
                

    

            
        
        
       
                
                    
                
            
            
        

            
            
                
            
            
        
                
        
                
                
            
        
            
                
                
                    
                
                
        
        


        
        
        
        

            
                    
            
                    
        
 

                
        
        

            
        
        
                
            
                
     
        
        
                
                
        
        
        
        
                
        

            
                
            


        
                
            
            
            
            
                    
        















    #<--Solving Area Ends
    endtime=datetime.datetime.now()
    time=(endtime-starttime).total_seconds()*1000
    if(os.path.exists('input.txt')):
        print("Time:",time,"ms")  
    
                
class FastReader(io.IOBase):
    newlines = 0

    def __init__(self, fd, chunk_size=1024 * 8):
        self._fd = fd
        self._chunk_size = chunk_size
        self.buffer = io.BytesIO()

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, self._chunk_size))
            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, size=-1):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, self._chunk_size if size == -1 else size))
            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()


class FastWriter(io.IOBase):

    def __init__(self, fd):
        self._fd = fd
        self.buffer = io.BytesIO()
        self.write = self.buffer.write

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


class FastStdin(io.IOBase):
    def __init__(self, fd=0):
        self.buffer = FastReader(fd)
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


class FastStdout(io.IOBase):
    def __init__(self, fd=1):
        self.buffer = FastWriter(fd)
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.flush = self.buffer.flush


if __name__ == '__main__':
    sys.stdin = FastStdin()
    sys.stdout = FastStdout()
    main()