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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\'' << x << '\''; }
void __print(const char *x) { cerr << '\"' << x << '\"'; }
void __print(const string &x) { cerr << '\"' << x << '\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V> &x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T>
void __print(const T &x) {
  int f = 0;
  cerr << '{';
  for (auto &i : x) cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
long long binpow(long long x, long long y) {
  long long res = 1;
  while (y > 0) {
    if (y & 1) res = (res * x);
    y = y >> 1;
    x = (x * x);
  }
  return res;
}
long long binpowmod(long long x, long long y, long long p) {
  long long res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
long long mod_inverse(long long n, long long p) {
  return binpowmod(n, p - 2, p);
}
long long gcd(long long x, long long y) {
  if (y == 0) return x;
  return gcd(y, x % y);
}
bool comp_pairs_by_s(pair<long long, long long> &x,
                     pair<long long, long long> &y) {
  return x.second < y.second;
}
bool isPowerOfTwo(long long x) { return x && (!(x & (x - 1))); }
class cmp {
 public:
  bool operator()(pair<int, int> A, pair<int, int> B) {
    if (abs(A.first - A.second) == abs(B.first - B.second))
      return A.first > B.first;
    return abs(A.first - A.second) < abs(B.first - B.second);
  }
};
void swap(long long &x, long long &y) {
  int temp = x;
  x = y;
  y = temp;
}
unsigned int onesComplement(unsigned int n) {
  int number_of_bits = floor(log2(n)) + 1;
  return ((1 << number_of_bits) - 1) ^ n;
}
bool comp(pair<long long, long long> x, pair<long long, long long> y) {
  return x.second < y.second;
}
bool comp1(pair<long long, long long> x, pair<long long, long long> y) {
  return x.second < y.second;
}
void solve() {
  int n;
  cin >> n;
  string ss;
  cin >> ss;
  vector<int> ans(n + 1);
  vector<set<int>> s(2);
  for (int i = 0; i < n; ++i)
    if (ss[i] == '1')
      s[1].insert(i + 1);
    else
      s[0].insert(i + 1);
  int i = (ss[0] - '0') ^ 1;
  int prev = INT_MIN;
  int cnt = 0;
  while (!s[0].empty() || !s[1].empty()) {
    auto cur = s[i ^ 1].upper_bound(prev);
    if (cur == s[i ^ 1].end()) {
      cnt++;
      prev = min(*(s[0].begin()), *(s[1].begin()));
      if (prev == *(s[0].begin())) {
        ans[prev] = cnt + 1;
        s[0].erase(prev);
        i = 0;
      } else {
        ans[prev] = cnt + 1;
        s[1].erase(prev);
        i = 1;
      }
    } else {
      ans[*cur] = cnt + 1;
      i ^= 1;
      prev = *cur;
      s[i].erase(cur);
    }
  }
  cout << cnt + 1 << '\n';
  for (int i = 1; i <= n; ++i) cout << ans[i] << ' ';
  cout << '\n';
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t;
  cin >> t;
  while (t--) solve();
}