Problem: There is a bridge that connects the left and right banks of a river. There are 2 N doors placed at different positions on this bridge, painted in some colors. The colors of the doors are represented by integers from 1 through N. For each k (1 \leq k \leq N), there are exactly two doors painted in Color k.

Snuke decides to cross the bridge from the left bank to the right bank. He will keep on walking to the right, but the following event will happen while doing so:

* At the moment Snuke touches a door painted in Color k (1 \leq k \leq N), he teleports to the right side of the other door painted in Color k.



It can be shown that he will eventually get to the right bank.

For each i (1 \leq i \leq 2 N - 1), the section between the i-th and (i + 1)-th doors from the left will be referred to as Section i. After crossing the bridge, Snuke recorded whether or not he walked through Section i, for each i (1 \leq i \leq 2 N - 1). This record is given to you as a string s of length 2 N - 1. For each i (1 \leq i \leq 2 N - 1), if Snuke walked through Section i, the i-th character in s is `1`; otherwise, the i-th character is `0`.

<image>

Figure: A possible arrangement of doors for Sample Input 3

Determine if there exists an arrangement of doors that is consistent with the record. If it exists, construct one such arrangement.

Constraints

* 1 \leq N \leq 10^5
* |s| = 2 N - 1
* s consists of `0` and `1`.

Input

Input is given from Standard Input in the following format:


N
s


Output

If there is no arrangement of doors that is consistent with the record, print `No`. If there exists such an arrangement, print `Yes` in the first line, then print one such arrangement in the second line, in the following format:


c_1 c_2 ... c_{2 N}


Here, for each i (1 \leq i \leq 2 N), c_i is the color of the i-th door from the left.

Examples

Input

2
010


Output

Yes
1 1 2 2


Input

2
001


Output

No


Input

3
10110


Output

Yes
1 3 2 1 2 3


Input

3
10101


Output

No


Input

6
00111011100


Output

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

Solution (in CPP):

Solution:
#ifndef __clang__
#pragma GCC optimize "-O3"
#pragma GCC target "tune=native"
#endif
#ifdef ONLINE_JUDGE
#define NDEBUG 1
#endif
#include <stdio.h>
#include <bits/stdc++.h>

#define FOR(i, n)     for(lli i = 0; i < (lli)(n); ++i)
#define FORU(i, j, k) for(lli i = (j); i <= (lli)(k); ++i)
#define FORD(i, j, k) for(lli i = (j); i >= (lli)(k); --i)

#define SQ(x) ((x)*(x))

#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define eb emplace_back

using namespace std;

template<typename... As>
struct tpl : public std::tuple<As...> {
  using std::tuple<As...>::tuple;
  tpl(){}
  tpl(std::tuple<As...> const& b) { std::tuple<As...>::operator=(b); }

  template<typename T = tuple<As...> >
  typename tuple_element<0, T>::type const&
  x() const { return get<0>(*this); }
  template<typename T = tuple<As...> >
  typename tuple_element<0, T>::type&
  x() { return get<0>(*this); }

  template<typename T = tuple<As...> >
  typename tuple_element<1, T>::type const&
  y() const { return get<1>(*this); }
  template<typename T = tuple<As...> >
  typename tuple_element<1, T>::type&
  y() { return get<1>(*this); }

  template<typename T = tuple<As...> >
  typename tuple_element<2, T>::type const&
  z() const { return get<2>(*this); }
  template<typename T = tuple<As...> >
  typename tuple_element<2, T>::type&
  z() { return get<2>(*this); }

  template<typename T = tuple<As...> >
  typename tuple_element<3, T>::type const&
  w() const { return get<3>(*this); }
  template<typename T = tuple<As...> >
  typename tuple_element<3, T>::type&
  w() { return get<3>(*this); }
};

using lli   = long long int;
using llu   = long long unsigned;

using pii   = tpl<lli, lli>;
using piii  = tpl<lli, lli, lli>;
using piiii = tpl<lli, lli, lli, lli>;
using vi    = vector<lli>;
using vii   = vector<pii>;
using viii  = vector<piii>;
using vvi   = vector<vi>;
using vvii  = vector<vii>;
using vviii = vector<viii>;

template<class T>
using min_queue = priority_queue<T, vector<T>, greater<T> >;
template<class T>
using max_queue = priority_queue<T>;

template<size_t... I>
struct my_index_sequence {
  using type = my_index_sequence;
  static constexpr array<size_t, sizeof...(I)> value = { {I...} };
};

namespace my_index_sequence_detail {
  template<typename I, typename J> struct concat;
  template<size_t... I, size_t... J>
  struct concat<my_index_sequence<I...>, my_index_sequence<J...> > :
    my_index_sequence<I..., (sizeof...(I)+J)...> { };
  template<size_t N> struct make_index_sequence :
    concat<typename make_index_sequence<N/2>::type, typename make_index_sequence<N-N/2>::type>::type { };
  template <> struct make_index_sequence<0> : my_index_sequence<>{};
  template <> struct make_index_sequence<1> : my_index_sequence<0>{};
}

template<class... A>
using my_index_sequence_for = typename my_index_sequence_detail::make_index_sequence<sizeof...(A)>::type;

template<class T, size_t... I>
void print_tuple(ostream& s, T const& a, my_index_sequence<I...>){
  using swallow = int[];
  (void)swallow{0, (void(s << (I == 0? "" : ", ") << get<I>(a)), 0)...};
}

template<class T>
ostream& print_collection(ostream& s, T const& a);
template<class... A>
ostream& operator<<(ostream& s, tpl<A...> const& a);
template<class... A>
ostream& operator<<(ostream& s, tuple<A...> const& a);
template<class A, class B>
ostream& operator<<(ostream& s, pair<A, B> const& a);

template<class T, size_t I>
ostream& operator<<(ostream& s, array<T, I> const& a) { return print_collection(s, a); }
template<class T>
ostream& operator<<(ostream& s, vector<T> const& a) { return print_collection(s, a); }
template<class T, class U>
ostream& operator<<(ostream& s, multimap<T, U> const& a) { return print_collection(s, a); }
template<class T>
ostream& operator<<(ostream& s, multiset<T> const& a) { return print_collection(s, a); }
template<class T, class U>
ostream& operator<<(ostream& s, map<T, U> const& a) { return print_collection(s, a); }
template<class T>
ostream& operator<<(ostream& s, set<T> const& a) { return print_collection(s, a); }

template<class T>
ostream& print_collection(ostream& s, T const& a){
  s << '[';
  for(auto it = begin(a); it != end(a); ++it){
    s << *it;
    if(it != prev(end(a))) s << " ";
  }
  return s << ']';
}

template<class... A>
ostream& operator<<(ostream& s, tpl<A...> const& a){
  s << '(';
  print_tuple(s, a, my_index_sequence_for<A...>{});
  return s << ')';
}

template<class... A>
ostream& operator<<(ostream& s, tuple<A...> const& a){
  s << '(';
  print_tuple(s, a, my_index_sequence_for<A...>{});
  return s << ')';
}

template<class A, class B>
ostream& operator<<(ostream& s, pair<A, B> const& a){
  return s << "(" << get<0>(a) << ", " << get<1>(a) << ")";
}

//------------------------------------------------------------------------------

int C[200000];

void fail(){
  cout << "No" << endl;
  exit(0);
}

void output(int n) {
  cout << "Yes" << endl;
  FOR(i,2*n) cout << C[i] << ' ';
  cout << endl;
  exit(0);
}

int main(){
  ios::sync_with_stdio(0); cin.tie(0);
  int n; cin>>n;
  string s; cin>>s;
  s = '1'+s+'1';
  vi ins, outs;
  vi gates, other;
  FOR(i,2*n) {
    if(s[i] == '0') {
      if(s[i+1] == '0') {
        other.pb(i);
      }else{
        outs.pb(i);
      }
    }else{
      if(s[i+1] == '0') {
        ins.pb(i);
      }else{
        gates.pb(i);
      }
    }
  }
  FOR(i,2*n) C[i] = -1;
  if(ins.size() != outs.size() || (gates.size()&1) || (other.size()&1)) fail();
  int nc = 1;
  FOR(j,other.size()/2) {
    C[other[2*j]] = C[other[2*j+1]] = nc++;
  }
  if(gates.size()%4 == 0) {
    FOR(i,ins.size()) C[ins[i]] = C[outs[i]] = nc++;
    FOR(i,gates.size()/4) {
      C[gates[4*i]] = C[gates[4*i+2]] = nc++;
      C[gates[4*i+1]] = C[gates[4*i+3]] = nc++;
    }
    output(n);
    return 0;
  }
  int i0 = -1;
  int k0 = -1;
  FOR(i,2*n) {
    if(s[i] == '1' && s[i+1] == '1' && i0 != -1) {
      k0 = i;
      break;
    }
    if(s[i] == '0' && s[i+1] == '1') {
      i0 = i;
    }
  }
  if(i0 == -1 || k0 == -1) fail();
  int j0 = k0;
  while(1) {
    if(j0 == 2*n) fail();
    if(s[j0] == '1' && s[j0+1] == '0') break;
    j0++;
  }
  C[i0] = C[j0] = nc++;
  int k1 = -1;
  for(int k : gates) if(k < i0 || k > j0) {
      k1 = k;
      break;
    }
  if(k1 == -1) fail();
  C[k0] = C[k1] = nc++;
  vi gates2, ins2, outs2;
  { int i = 0;
    { if(i == k0) i = k1;
      else if(i == k1) i = k0;
      else if(i == i0) i = j0;
      else if(i == j0) i = i0;
    }
    while(i < 2*n) {
      if(C[i] == -1) {
        if(s[i] == '0' && s[i+1] == '1') ins2.pb(i);
        else if(s[i] == '1' && s[i+1] == '0') outs2.pb(i);
        else if(s[i] == '1' && s[i+1] == '1') gates2.pb(i);
      }
      i += 1;
      if(i == k0) i = k1;
      else if(i == k1) i = k0;
      else if(i == i0) i = j0;
      else if(i == j0) i = i0;
    }
  }
  FOR(i,ins2.size()) C[ins2[i]] = C[outs2[i]] = nc++;
  FOR(i,gates2.size()/4) {
    C[gates2[4*i]] = C[gates2[4*i+2]] = nc++;
    C[gates2[4*i+1]] = C[gates2[4*i+3]] = nc++;
  }
  output(n);
  return 0;
}