#include <bits/stdc++.h>
using namespace std;
namespace tourist {
template <typename T>
class graph {
 public:
  struct edge {
    int from;
    int to;
    T cost;
  };
  vector<edge> edges;
  vector<vector<int>> g;
  int n;
  graph(int _n) : n(_n) { g.resize(n); }
  virtual int add(int from, int to, T cost) = 0;
};
template <typename T>
class undigraph : public graph<T> {
 public:
  using graph<T>::edges;
  using graph<T>::g;
  using graph<T>::n;
  undigraph(int _n) : graph<T>(_n) {}
  int add(int from, int to, T cost = 1) {
    assert(0 <= from && from < n && 0 <= to && to < n);
    int id = (int)edges.size();
    g[from].push_back(id);
    g[to].push_back(id);
    edges.push_back({from, to, cost});
    return id;
  }
};
template <typename T>
vector<int> find_max_unweighted_matching(const undigraph<T> &g) {
  vector<int> mate(g.n, -1);
  vector<int> label(g.n);
  vector<int> parent(g.n);
  vector<int> orig(g.n);
  queue<int> q;
  vector<int> aux(g.n, -1);
  int aux_time = -1;
  auto lca = [&](int x, int y) {
    aux_time++;
    while (true) {
      if (x != -1) {
        if (aux[x] == aux_time) {
          return x;
        }
        aux[x] = aux_time;
        if (mate[x] == -1) {
          x = -1;
        } else {
          x = orig[parent[mate[x]]];
        }
      }
      swap(x, y);
    }
  };
  auto blossom = [&](int v, int w, int a) {
    while (orig[v] != a) {
      parent[v] = w;
      w = mate[v];
      if (label[w] == 1) {
        label[w] = 0;
        q.push(w);
      }
      orig[v] = orig[w] = a;
      v = parent[w];
    }
  };
  auto augment = [&](int v) {
    while (v != -1) {
      int pv = parent[v];
      int nv = mate[pv];
      mate[v] = pv;
      mate[pv] = v;
      v = nv;
    }
  };
  auto bfs = [&](int root) {
    fill(label.begin(), label.end(), -1);
    iota(orig.begin(), orig.end(), 0);
    while (!q.empty()) {
      q.pop();
    }
    q.push(root);
    label[root] = 0;
    while (!q.empty()) {
      int v = q.front();
      q.pop();
      for (int id : g.g[v]) {
        auto &e = g.edges[id];
        int x = e.from ^ e.to ^ v;
        if (label[x] == -1) {
          label[x] = 1;
          parent[x] = v;
          if (mate[x] == -1) {
            augment(x);
            return true;
          }
          label[mate[x]] = 0;
          q.push(mate[x]);
          continue;
        }
        if (label[x] == 0 && orig[v] != orig[x]) {
          int a = lca(orig[v], orig[x]);
          blossom(x, v, a);
          blossom(v, x, a);
        }
      }
    }
    return false;
  };
  auto greedy = [&]() {
    vector<int> order(g.n);
    iota(order.begin(), order.end(), 0);
    shuffle(order.begin(), order.end(), mt19937(787788));
    for (int i : order) {
      if (mate[i] == -1) {
        for (int id : g.g[i]) {
          auto &e = g.edges[id];
          int to = e.from ^ e.to ^ i;
          if (mate[to] == -1) {
            mate[i] = to;
            mate[to] = i;
            break;
          }
        }
      }
    }
  };
  greedy();
  for (int i = 0; i < g.n; i++) {
    if (mate[i] == -1) {
      bfs(i);
    }
  }
  return mate;
}
}  // namespace tourist
const int N = 300005;
int n, a[N], eid, root, f1[605][605];
tuple<int, int, int, int> f2[605][605];
bool vis[N];
vector<tuple<int, int, int, int>> e[605];
struct ufs {
  int fa[605], tag[605];
  ufs() {
    for (int i = (1); i <= (604); ++i) fa[i] = i;
  }
  int fd(int k1) { return fa[k1] == k1 ? k1 : fa[k1] = fd(fa[k1]); }
  bool mer(int u, int v) {
    u = fd(u), v = fd(v);
    if (u == v) {
      if (tag[u]) return 0;
      tag[u] = 1;
      return 1;
    } else {
      if (tag[u] && tag[v]) return 0;
      tag[v] |= tag[u], fa[u] = v;
      return 1;
    }
  }
} o1;
int used[N], nowt;
void get_root(int u, int last) {
  if (used[u] == nowt) return;
  used[u] = nowt;
  for (auto &x : e[u])
    if (get<3>(x) != last) {
      if (used[get<0>(x)] == nowt) root = get<0>(x);
      get_root(get<0>(x), get<3>(x));
    }
}
void deal(int u, int last) {
  for (auto &x : e[u])
    if (get<3>(x) != last) {
      if (used[get<3>(x)] == nowt) continue;
      used[get<3>(x)] = nowt;
      if (!vis[get<0>(x)]) {
        if (!a[get<2>(x)]) a[get<2>(x)] = get<0>(x), vis[get<0>(x)] = 1;
      } else {
        if (!a[get<1>(x)]) a[get<1>(x)] = u, vis[u] = 1;
      }
      deal(get<0>(x), get<3>(x));
    }
}
void color(int u, int last) {
  for (auto &x : e[u])
    if (get<3>(x) != last) {
      if (!a[get<2>(x)]) a[get<2>(x)] = get<0>(x);
      color(get<0>(x), get<3>(x));
    }
}
int main() {
  scanf("%d", &n);
  for (int i = (1); i <= (n); ++i) scanf("%d", &a[i]);
  vis[0] = 1;
  for (int i = (1); i <= (n - 1); ++i) {
    if (a[i] && a[i + 1] && a[i] == a[i + 1]) {
      vis[a[i]] = 1;
    }
  }
  while (1) {
    bool flg = 0;
    for (int i = 1, j; i <= n; i = j) {
      j = i + 1;
      while (j <= n && (!!a[i]) == (!!a[j])) ++j;
      if (!a[i]) {
        int u = vis[a[i - 1]] ? 0 : a[i - 1], u_ = i, v = vis[a[j]] ? 0 : a[j],
            v_ = j - 1;
        if ((j - i) & 1) {
          if (!u && !v) {
          } else if (!u) {
            a[v_] = v;
            vis[v] = 1;
            flg = 1;
          } else if (!v || u == v) {
            a[u_] = u;
            vis[u] = 1;
            flg = 1;
          } else {
          }
        }
      }
    }
    if (!flg) break;
  }
  for (int i = 1, j; i <= n; i = j) {
    j = i + 1;
    while (j <= n && (!!a[i]) == (!!a[j])) ++j;
    if (!a[i]) {
      int u = vis[a[i - 1]] ? 0 : a[i - 1], u_ = i, v = vis[a[j]] ? 0 : a[j],
          v_ = j - 1;
      if ((j - i) & 1) {
        if (!u && !v) {
        } else if (!u) {
        } else if (!v || u == v) {
        } else {
          if (o1.mer(u, v)) {
            e[u].emplace_back(v, u_, v_, ++eid);
            e[v].emplace_back(u, v_, u_, eid);
          }
        }
      }
    }
  }
  for (int i = (1); i <= (600); ++i)
    if (o1.fd(i) == i && o1.tag[i]) {
      root = i;
      ++nowt;
      get_root(i, 0);
      ++nowt;
      deal(root, 0);
    }
  tourist::undigraph<int> g(605);
  for (int i = 1, j; i <= n; i = j) {
    j = i + 1;
    while (j <= n && (!!a[i]) == (!!a[j])) ++j;
    if (!a[i]) {
      int u = vis[a[i - 1]] ? 0 : a[i - 1], u_ = i, v = vis[a[j]] ? 0 : a[j],
          v_ = j - 1;
      if (~(j - i) & 1) {
        if (!u && !v) {
        } else if (!u) {
        } else if (!v || u == v) {
        } else if (o1.fd(u) != o1.fd(v)) {
          if (o1.fd(u) > o1.fd(v)) swap(u, v), swap(u_, v_);
          if (!o1.tag[o1.fd(u)] && !o1.tag[o1.fd(v)]) {
            if (!f1[o1.fd(u)][o1.fd(v)]) {
              f1[o1.fd(u)][o1.fd(v)] = 1;
              f2[o1.fd(u)][o1.fd(v)] = {u, u_, v, v_};
              g.add(o1.fd(u), o1.fd(v));
            }
          }
        }
      }
    }
  }
  auto ps = [&](int u) {
    assert(!o1.tag[o1.fd(u)]);
    o1.tag[o1.fd(u)] = 1;
    color(u, 0);
  };
  vector<int> mate(tourist::find_max_unweighted_matching(g));
  for (int i = (1); i <= (600); ++i)
    if (mate[i] != -1 && i < mate[i]) {
      assert(f1[i][mate[i]]);
      int u, u_, v, v_;
      tie(u, u_, v, v_) = f2[i][mate[i]];
      a[u_] = u, a[v_] = v;
      ps(u);
      ps(v);
    }
  for (int i = (1); i <= (600); ++i)
    if (o1.fd(i) == i && !o1.tag[i]) {
      color(i, 0);
    }
  for (int i = (1); i <= (n - 1); ++i)
    if (a[i] && a[i + 1] && a[i] == a[i + 1]) vis[a[i]] = 1;
  int cur = n;
  for (int i = (1); i <= (n - 1); ++i)
    if (!a[i] && !a[i + 1]) {
      while (cur >= 1 && vis[cur]) --cur;
      vis[cur] = 1;
      a[i] = a[i + 1] = cur;
    }
  for (int i = (1); i <= (n); ++i)
    if (!a[i]) {
      a[i] = n;
    }
  for (int i = (1); i <= (n); ++i) printf("%d%c", a[i], i == n ? '\n' : ' ');
  return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

You are given an array a consisting of n non-negative integers.

You have to replace each 0 in a with an integer from 1 to n (different elements equal to 0 can be replaced by different integers).

The value of the array you obtain is the number of integers k from 1 to n such that the following condition holds: there exist a pair of adjacent elements equal to k (i. e. there exists some i ∈ [1, n - 1] such that a_i = a_{i + 1} = k). If there are multiple such pairs for some integer k, this integer is counted in the value only once.

Your task is to obtain the array with the maximum possible value.

Input

The first line contains one integer n (2 ≤ n ≤ 3 ⋅ 10^5) — the number of elements in the array.

The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ min(n, 600)) — the elements of the array.

Output

Print n integers not less than 1 and not greater than n — the array with the maximum possible value you can obtain.

If there are multiple answers, print any of them.

Examples

Input


4
1 1 0 2


Output


1 1 2 2 


Input


5
0 0 0 0 0


Output


3 1 1 3 3


Input


5
1 2 3 4 5


Output


1 2 3 4 5 


Input


6
1 0 0 0 0 1


Output


1 2 3 3 1 1


Input


3
3 0 2


Output


3 2 2 


Input


5
1 0 2 0 1


Output


1 2 2 1 1 


Input


7
1 0 2 3 1 0 2


Output


1 2 2 3 1 1 2 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
namespace tourist {
template <typename T>
class graph {
 public:
  struct edge {
    int from;
    int to;
    T cost;
  };
  vector<edge> edges;
  vector<vector<int>> g;
  int n;
  graph(int _n) : n(_n) { g.resize(n); }
  virtual int add(int from, int to, T cost) = 0;
};
template <typename T>
class undigraph : public graph<T> {
 public:
  using graph<T>::edges;
  using graph<T>::g;
  using graph<T>::n;
  undigraph(int _n) : graph<T>(_n) {}
  int add(int from, int to, T cost = 1) {
    assert(0 <= from && from < n && 0 <= to && to < n);
    int id = (int)edges.size();
    g[from].push_back(id);
    g[to].push_back(id);
    edges.push_back({from, to, cost});
    return id;
  }
};
template <typename T>
vector<int> find_max_unweighted_matching(const undigraph<T> &g) {
  vector<int> mate(g.n, -1);
  vector<int> label(g.n);
  vector<int> parent(g.n);
  vector<int> orig(g.n);
  queue<int> q;
  vector<int> aux(g.n, -1);
  int aux_time = -1;
  auto lca = [&](int x, int y) {
    aux_time++;
    while (true) {
      if (x != -1) {
        if (aux[x] == aux_time) {
          return x;
        }
        aux[x] = aux_time;
        if (mate[x] == -1) {
          x = -1;
        } else {
          x = orig[parent[mate[x]]];
        }
      }
      swap(x, y);
    }
  };
  auto blossom = [&](int v, int w, int a) {
    while (orig[v] != a) {
      parent[v] = w;
      w = mate[v];
      if (label[w] == 1) {
        label[w] = 0;
        q.push(w);
      }
      orig[v] = orig[w] = a;
      v = parent[w];
    }
  };
  auto augment = [&](int v) {
    while (v != -1) {
      int pv = parent[v];
      int nv = mate[pv];
      mate[v] = pv;
      mate[pv] = v;
      v = nv;
    }
  };
  auto bfs = [&](int root) {
    fill(label.begin(), label.end(), -1);
    iota(orig.begin(), orig.end(), 0);
    while (!q.empty()) {
      q.pop();
    }
    q.push(root);
    label[root] = 0;
    while (!q.empty()) {
      int v = q.front();
      q.pop();
      for (int id : g.g[v]) {
        auto &e = g.edges[id];
        int x = e.from ^ e.to ^ v;
        if (label[x] == -1) {
          label[x] = 1;
          parent[x] = v;
          if (mate[x] == -1) {
            augment(x);
            return true;
          }
          label[mate[x]] = 0;
          q.push(mate[x]);
          continue;
        }
        if (label[x] == 0 && orig[v] != orig[x]) {
          int a = lca(orig[v], orig[x]);
          blossom(x, v, a);
          blossom(v, x, a);
        }
      }
    }
    return false;
  };
  auto greedy = [&]() {
    vector<int> order(g.n);
    iota(order.begin(), order.end(), 0);
    shuffle(order.begin(), order.end(), mt19937(787788));
    for (int i : order) {
      if (mate[i] == -1) {
        for (int id : g.g[i]) {
          auto &e = g.edges[id];
          int to = e.from ^ e.to ^ i;
          if (mate[to] == -1) {
            mate[i] = to;
            mate[to] = i;
            break;
          }
        }
      }
    }
  };
  greedy();
  for (int i = 0; i < g.n; i++) {
    if (mate[i] == -1) {
      bfs(i);
    }
  }
  return mate;
}
}  // namespace tourist
const int N = 300005;
int n, a[N], eid, root, f1[605][605];
tuple<int, int, int, int> f2[605][605];
bool vis[N];
vector<tuple<int, int, int, int>> e[605];
struct ufs {
  int fa[605], tag[605];
  ufs() {
    for (int i = (1); i <= (604); ++i) fa[i] = i;
  }
  int fd(int k1) { return fa[k1] == k1 ? k1 : fa[k1] = fd(fa[k1]); }
  bool mer(int u, int v) {
    u = fd(u), v = fd(v);
    if (u == v) {
      if (tag[u]) return 0;
      tag[u] = 1;
      return 1;
    } else {
      if (tag[u] && tag[v]) return 0;
      tag[v] |= tag[u], fa[u] = v;
      return 1;
    }
  }
} o1;
int used[N], nowt;
void get_root(int u, int last) {
  if (used[u] == nowt) return;
  used[u] = nowt;
  for (auto &x : e[u])
    if (get<3>(x) != last) {
      if (used[get<0>(x)] == nowt) root = get<0>(x);
      get_root(get<0>(x), get<3>(x));
    }
}
void deal(int u, int last) {
  for (auto &x : e[u])
    if (get<3>(x) != last) {
      if (used[get<3>(x)] == nowt) continue;
      used[get<3>(x)] = nowt;
      if (!vis[get<0>(x)]) {
        if (!a[get<2>(x)]) a[get<2>(x)] = get<0>(x), vis[get<0>(x)] = 1;
      } else {
        if (!a[get<1>(x)]) a[get<1>(x)] = u, vis[u] = 1;
      }
      deal(get<0>(x), get<3>(x));
    }
}
void color(int u, int last) {
  for (auto &x : e[u])
    if (get<3>(x) != last) {
      if (!a[get<2>(x)]) a[get<2>(x)] = get<0>(x);
      color(get<0>(x), get<3>(x));
    }
}
int main() {
  scanf("%d", &n);
  for (int i = (1); i <= (n); ++i) scanf("%d", &a[i]);
  vis[0] = 1;
  for (int i = (1); i <= (n - 1); ++i) {
    if (a[i] && a[i + 1] && a[i] == a[i + 1]) {
      vis[a[i]] = 1;
    }
  }
  while (1) {
    bool flg = 0;
    for (int i = 1, j; i <= n; i = j) {
      j = i + 1;
      while (j <= n && (!!a[i]) == (!!a[j])) ++j;
      if (!a[i]) {
        int u = vis[a[i - 1]] ? 0 : a[i - 1], u_ = i, v = vis[a[j]] ? 0 : a[j],
            v_ = j - 1;
        if ((j - i) & 1) {
          if (!u && !v) {
          } else if (!u) {
            a[v_] = v;
            vis[v] = 1;
            flg = 1;
          } else if (!v || u == v) {
            a[u_] = u;
            vis[u] = 1;
            flg = 1;
          } else {
          }
        }
      }
    }
    if (!flg) break;
  }
  for (int i = 1, j; i <= n; i = j) {
    j = i + 1;
    while (j <= n && (!!a[i]) == (!!a[j])) ++j;
    if (!a[i]) {
      int u = vis[a[i - 1]] ? 0 : a[i - 1], u_ = i, v = vis[a[j]] ? 0 : a[j],
          v_ = j - 1;
      if ((j - i) & 1) {
        if (!u && !v) {
        } else if (!u) {
        } else if (!v || u == v) {
        } else {
          if (o1.mer(u, v)) {
            e[u].emplace_back(v, u_, v_, ++eid);
            e[v].emplace_back(u, v_, u_, eid);
          }
        }
      }
    }
  }
  for (int i = (1); i <= (600); ++i)
    if (o1.fd(i) == i && o1.tag[i]) {
      root = i;
      ++nowt;
      get_root(i, 0);
      ++nowt;
      deal(root, 0);
    }
  tourist::undigraph<int> g(605);
  for (int i = 1, j; i <= n; i = j) {
    j = i + 1;
    while (j <= n && (!!a[i]) == (!!a[j])) ++j;
    if (!a[i]) {
      int u = vis[a[i - 1]] ? 0 : a[i - 1], u_ = i, v = vis[a[j]] ? 0 : a[j],
          v_ = j - 1;
      if (~(j - i) & 1) {
        if (!u && !v) {
        } else if (!u) {
        } else if (!v || u == v) {
        } else if (o1.fd(u) != o1.fd(v)) {
          if (o1.fd(u) > o1.fd(v)) swap(u, v), swap(u_, v_);
          if (!o1.tag[o1.fd(u)] && !o1.tag[o1.fd(v)]) {
            if (!f1[o1.fd(u)][o1.fd(v)]) {
              f1[o1.fd(u)][o1.fd(v)] = 1;
              f2[o1.fd(u)][o1.fd(v)] = {u, u_, v, v_};
              g.add(o1.fd(u), o1.fd(v));
            }
          }
        }
      }
    }
  }
  auto ps = [&](int u) {
    assert(!o1.tag[o1.fd(u)]);
    o1.tag[o1.fd(u)] = 1;
    color(u, 0);
  };
  vector<int> mate(tourist::find_max_unweighted_matching(g));
  for (int i = (1); i <= (600); ++i)
    if (mate[i] != -1 && i < mate[i]) {
      assert(f1[i][mate[i]]);
      int u, u_, v, v_;
      tie(u, u_, v, v_) = f2[i][mate[i]];
      a[u_] = u, a[v_] = v;
      ps(u);
      ps(v);
    }
  for (int i = (1); i <= (600); ++i)
    if (o1.fd(i) == i && !o1.tag[i]) {
      color(i, 0);
    }
  for (int i = (1); i <= (n - 1); ++i)
    if (a[i] && a[i + 1] && a[i] == a[i + 1]) vis[a[i]] = 1;
  int cur = n;
  for (int i = (1); i <= (n - 1); ++i)
    if (!a[i] && !a[i + 1]) {
      while (cur >= 1 && vis[cur]) --cur;
      vis[cur] = 1;
      a[i] = a[i + 1] = cur;
    }
  for (int i = (1); i <= (n); ++i)
    if (!a[i]) {
      a[i] = n;
    }
  for (int i = (1); i <= (n); ++i) printf("%d%c", a[i], i == n ? '\n' : ' ');
  return 0;
}

```