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;
const int INF = 0x3f3f3f3f, MAXN = 1e6 + 50;
const long long LINF = 0x3f3f3f3f3f3f3f3f, MOD = 1e9 + 7;
const double Pi = acos(-1), EPS = 1e-6;
void test() { cerr << "\n"; }
template <typename T, typename... Args>
void test(T x, Args... args) {
  cerr << x << " ";
  test(args...);
}
inline long long qpow(long long a, long long b) {
  return b ? ((b & 1) ? a * qpow(a * a % MOD, b >> 1) % MOD
                      : qpow(a * a % MOD, b >> 1)) %
                 MOD
           : 1;
}
inline long long qpow(long long a, long long b, long long c) {
  return b ? ((b & 1) ? a * qpow(a * a % c, b >> 1, c) % c
                      : qpow(a * a % c, b >> 1, c)) %
                 c
           : 1;
}
inline long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; }
inline long long cede(long long a, long long b) {
  if (b < 0) return cede(-a, -b);
  if (a < 0) return a / b;
  return (a + b - 1) / b;
}
inline long long flde(long long a, long long b) {
  if (b < 0) return flde(-a, -b);
  if (a < 0) return (a - b + 1) / b;
  return a / b;
}
inline int sign(double x) { return x < -EPS ? -1 : x > EPS; }
inline int dbcmp(double l, double r) { return sign(l - r); }
namespace Fast_IO {
const int MAXL((1 << 18) + 1);
int iof, iotp;
char ioif[MAXL], *ioiS, *ioiT, ioof[MAXL],
    *iooS = ioof, *iooT = ioof + MAXL - 1, ioc, iost[55];
char Getchar() {
  if (ioiS == ioiT) {
    ioiS = ioif;
    ioiT = ioiS + fread(ioif, 1, MAXL, stdin);
    return (ioiS == ioiT ? EOF : *ioiS++);
  } else
    return (*ioiS++);
}
void Write() {
  fwrite(ioof, 1, iooS - ioof, stdout);
  iooS = ioof;
}
void Putchar(char x) {
  *iooS++ = x;
  if (iooS == iooT) Write();
}
inline int read() {
  int x = 0;
  for (iof = 1, ioc = Getchar(); (ioc < '0' || ioc > '9') && ioc != EOF;)
    iof = ioc == '-' ? -1 : 1, ioc = Getchar();
  if (ioc == EOF) Write(), exit(0);
  for (x = 0; ioc <= '9' && ioc >= '0'; ioc = Getchar())
    x = (x << 3) + (x << 1) + (ioc ^ 48);
  return x * iof;
}
inline long long read_ll() {
  long long x = 0;
  for (iof = 1, ioc = Getchar(); (ioc < '0' || ioc > '9') && ioc != EOF;)
    iof = ioc == '-' ? -1 : 1, ioc = Getchar();
  if (ioc == EOF) Write(), exit(0);
  for (x = 0; ioc <= '9' && ioc >= '0'; ioc = Getchar())
    x = (x << 3) + (x << 1) + (ioc ^ 48);
  return x * iof;
}
void Getstr(char *s, int &l) {
  for (ioc = Getchar(); ioc == ' ' || ioc == '\n' || ioc == '\t';)
    ioc = Getchar();
  if (ioc == EOF) Write(), exit(0);
  for (l = 0; !(ioc == ' ' || ioc == '\n' || ioc == '\t' || ioc == EOF);
       ioc = Getchar())
    s[l++] = ioc;
  s[l] = 0;
}
template <class Int>
void Print(Int x, char ch = '\0') {
  if (!x) Putchar('0');
  if (x < 0) Putchar('-'), x = -x;
  while (x) iost[++iotp] = x % 10 + '0', x /= 10;
  while (iotp) Putchar(iost[iotp--]);
  if (ch) Putchar(ch);
}
void Putstr(const char *s) {
  for (int i = 0, n = strlen(s); i < n; ++i) Putchar(s[i]);
}
}  // namespace Fast_IO
using namespace Fast_IO;
char str[MAXN];
queue<int> q0, q1;
vector<int> ans;
void work() {
  int n = read();
  int tmp;
  ans.clear();
  while (!q0.empty()) q0.pop();
  while (!q1.empty()) q1.pop();
  Getstr(str, tmp);
  int cntS = 0;
  for (int i = 0; i < n; i++) {
    if (str[i] == '0') {
      if (q0.empty()) {
        q1.push(++cntS);
        ans.push_back(cntS);
      } else {
        int tmp = q0.front();
        q0.pop();
        ans.push_back(tmp);
        q1.push(tmp);
      }
    } else {
      if (q1.empty()) {
        q0.push(++cntS);
        ans.push_back(cntS);
      } else {
        int tmp = q1.front();
        q1.pop();
        ans.push_back(tmp);
        q0.push(tmp);
      }
    }
  }
  printf("%d\n", cntS);
  for (auto x : ans) printf("%d ", x);
  printf("\n");
}
int main() {
  int T = read();
  for (int cas = 1; cas <= T; cas++) work();
}