#include <bits/stdc++.h>
using namespace std;
template <typename T>
void read(T &t) {
  t = 0;
  char ch = getchar();
  int f = 1;
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  do {
    (t *= 10) += ch - '0';
    ch = getchar();
  } while ('0' <= ch && ch <= '9');
  t *= f;
}
template <typename T>
void write(T t) {
  if (t < 0) {
    putchar('-');
    write(-t);
    return;
  }
  if (t > 9) write(t / 10);
  putchar('0' + t % 10);
}
template <typename T>
void writeln(T t) {
  write(t);
  puts("");
}
const int maxn = 610;
const int maxm = 300010;
int n, a[maxm];
namespace xyr {
const int maxm = 1000000;
int n, tot, head[maxn], id[610][610];
int nxt[maxm], to[maxm], ans;
void Add(int x, int y) {
  tot++;
  nxt[tot] = head[x];
  head[x] = tot;
  to[tot] = y;
}
void add(int x, int y, int z) {
  if (id[x][y]) return;
  id[x][y] = id[y][x] = z;
  Add(x, y);
  Add(y, x);
}
int match[maxn], pre[maxn], vis[maxn], fa[maxn];
queue<int> q;
int find(int x) {
  if (fa[x] == x) return x;
  return fa[x] = find(fa[x]);
}
int mk[maxn], cnt;
int lca(int x, int y) {
  cnt++;
  while (1) {
    if (x) {
      x = find(x);
      if (mk[x] == cnt) return x;
      mk[x] = cnt;
      x = pre[match[x]];
    }
    swap(x, y);
  }
}
void blossom(int x, int y, int z) {
  while (find(x) != z) {
    pre[x] = y;
    y = match[x];
    if (vis[y] == 2) vis[y] = 1, q.push(y);
    if (find(x) == x) fa[x] = z;
    if (find(y) == y) fa[y] = z;
    x = pre[y];
  }
}
int dfs(int s) {
  for (int i = 1; i <= n; i++) vis[i] = pre[i] = 0, fa[i] = i;
  q = queue<int>();
  q.push(s);
  vis[s] = 1;
  while (!q.empty()) {
    int u = q.front();
    q.pop();
    for (int i = head[u], v; i; i = nxt[i]) {
      v = to[i];
      if (find(u) == find(v) || vis[v] == 2) continue;
      if (!vis[v]) {
        vis[v] = 2;
        pre[v] = u;
        if (!match[v]) {
          for (int x = v, lst; x; x = lst)
            lst = match[pre[x]], match[x] = pre[x], match[pre[x]] = x;
          return 1;
        }
        vis[match[v]] = 1;
        q.push(match[v]);
      } else {
        int z = lca(u, v);
        blossom(u, v, z);
        blossom(v, u, z);
      }
    }
  }
  return 0;
}
void solve() {
  for (int i = n; i >= 1; i--)
    if (!match[i]) ans += dfs(i);
}
};  // namespace xyr
bool ban[610];
int mx, used[maxm];
vector<pair<int, int>> V, V2;
namespace BF {
vector<int> g[610];
int tim[610];
queue<int> q;
void link(int x, int y) { g[x].push_back(y), g[y].push_back(x); }
void solve() {
  for (int i = 1; i <= mx; i++) tim[i] = -1;
  for (int i = 1; i <= mx; i++)
    if (ban[i]) tim[i] = 0, q.push(i);
  while (!q.empty()) {
    int x = q.front();
    q.pop();
    for (int &y : g[x])
      if (tim[y] == -1) tim[y] = tim[x] + 1, q.push(y);
  }
}
};  // namespace BF
int dir[maxm], bel[maxn];
bool MK[maxm];
namespace Forest {
bool oncyc[610], vis[610];
int fa[610], from[610];
vector<pair<int, int>> g[610];
void add(int x, int y, int z) {
  g[x].push_back(make_pair(y, z)), g[y].push_back(make_pair(x, z));
}
int X, Y, Z;
vector<int> V[610];
int D[610], tot, S, dis[610];
void dfs(int x, int p, int w) {
  vis[x] = 1;
  fa[x] = p;
  from[x] = w;
  V[S].push_back(x);
  dis[x] = dis[p] + 1;
  for (auto [y, z] : g[x]) {
    if (z == from[x]) continue;
    if (vis[y]) {
      if (dis[x] > dis[y]) Y = x, X = y, Z = z;
    } else
      dfs(y, x, z);
  }
}
int VIS[610];
void DFS(int x, int f) {
  VIS[x] = 1;
  for (auto [y, z] : g[x])
    if (!oncyc[y] && z != f && !VIS[y]) {
      DFS(y, z);
      dir[z] = y;
    }
}
int TREE[610];
void solve() {
  for (int i = 1; i <= mx; i++)
    if (!vis[i]) {
      X = Y = 0;
      S = i;
      dfs(i, 0, -1);
      if (X) {
        tot = 0;
        dir[Z] = X;
        while (1) {
          D[++tot] = Y;
          if (Y == X) break;
          dir[from[Y]] = Y;
          Y = fa[Y];
        }
        for (int j = 1; j <= tot; j++) oncyc[D[j]] = 1;
        for (int j = 1; j <= tot; j++) DFS(D[j], 0);
      } else {
        TREE[i] = 1;
        for (int &x : V[i]) {
          bel[x] = i;
        }
      }
    }
  tot = 0;
}
int XYR[610];
void insert(int x) { XYR[bel[x]] = x; }
void insert(int x, int y) { insert(x), insert(y); }
void solve_again() {
  memset(vis, 0, sizeof(vis));
  for (int i = 1; i <= mx; i++)
    if (bel[i] == i && TREE[i]) {
      if (XYR[i]) {
        S = i;
        V[i].clear();
        dfs(XYR[i], 0, -1);
      } else
        XYR[i] = i;
      for (int &x : V[i])
        if (x != XYR[i]) dir[from[x]] = x;
    }
}
};  // namespace Forest
int now, R[maxm];
int GETNXT() {
  while (used[now]) now++;
  used[now] = 1;
  return now;
}
int main() {
  read(n);
  int F1 = 1, F2 = 1;
  for (int i = 1; i <= n; i++)
    read(a[i]), R[i] = a[i], mx = max(mx, a[i]), used[a[i]] = 1,
                F1 &= (a[i] == 0), F2 &= (a[i] != 0);
  if (F1) {
    for (int i = 0; i < n; i++) printf("%d ", i / 2 + 1);
    puts("");
    return 0;
  }
  if (F2) {
    for (int i = 1; i <= n; i++) printf("%d ", a[i]);
    puts("");
    return 0;
  }
  now = 1;
  for (int l = 1, r; l <= n; l = r + 1)
    if (!a[l]) {
      r = l;
      while (r < n && !a[r + 1]) r++;
      int x = a[l - 1], y = a[r + 1], len = r - l + 1;
      if (l == 1) {
        if (len & 1) {
          for (int i = 1; i < r; i += 2) a[i] = a[i + 1] = GETNXT();
          a[r] = a[r + 1];
        } else {
          for (int i = 1; i <= r; i += 2) a[i] = a[i + 1] = GETNXT();
        }
      } else if (r == n) {
        if (len & 1) {
          for (int i = l + 1; i <= n; i += 2) a[i] = a[i + 1] = GETNXT();
          a[l] = a[l - 1];
        } else {
          for (int i = l; i <= n; i += 2) a[i] = a[i + 1] = GETNXT();
        }
      } else {
        assert(x && y);
        if (x == y) {
          if (len & 1) {
            a[l] = a[l - 1];
            for (int i = l + 1; i <= r; i += 2) a[i] = a[i + 1] = GETNXT();
          } else {
            for (int i = l; i <= r; i += 2) a[i] = a[i + 1] = GETNXT();
          }
        } else {
          V.push_back(make_pair(l, r));
        }
      }
    } else
      r = l;
  for (int i = 1; i < n; i++)
    if (a[i] && a[i + 1] && a[i] == a[i + 1] && a[i] <= mx) ban[a[i]] = 1;
  for (pair<int, int> &A : V)
    if ((A.second - A.first + 1) % 2 == 1)
      BF::link(a[A.first - 1], a[A.second + 1]);
  BF::solve();
  for (int i = 1; i <= mx; i++) ban[i] = (BF::tim[i] != -1);
  for (auto [l, r] : V) {
    int x = a[l - 1], y = a[r + 1], len = r - l + 1;
    if (ban[y] && (!ban[x] || BF::tim[y] <= BF::tim[x])) {
      if (len & 1) {
        for (int i = l + 1; i <= r; i += 2) a[i] = a[i + 1] = GETNXT();
        a[l] = a[l - 1];
      } else {
        for (int i = l; i <= r; i += 2) a[i] = a[i + 1] = GETNXT();
      }
    } else if (ban[x] && (!ban[y] || BF::tim[y] >= BF::tim[x])) {
      if (len & 1) {
        for (int i = l; i < r; i += 2) a[i] = a[i + 1] = GETNXT();
        a[r] = a[r + 1];
      } else {
        for (int i = l; i <= r; i += 2) a[i] = a[i + 1] = GETNXT();
      }
    } else
      V2.push_back(make_pair(l, r));
  }
  for (int i = 0; i < V2.size(); i++) {
    int l = V2[i].first, r = V2[i].second, x = a[l - 1], y = a[r + 1],
        len = r - l + 1;
    if (len & 1) Forest::add(x, y, i);
  }
  Forest::solve();
  xyr::n = mx;
  for (int i = 0; i < V2.size(); i++) {
    int l = V2[i].first, r = V2[i].second, x = a[l - 1], y = a[r + 1],
        len = r - l + 1;
    if (len & 1 ^ 1) xyr::add(bel[x], bel[y], i + 1);
  }
  xyr::solve();
  for (int i = 1; i <= mx; i++)
    if (xyr::match[i] && xyr::match[i] < i) {
      int z = xyr::id[i][xyr::match[i]] - 1;
      MK[z] = 1;
      int x = a[V2[z].first - 1], y = a[V2[z].second + 1];
      Forest::insert(x, y);
    }
  Forest::solve_again();
  for (int i = 0; i < V2.size(); i++) {
    int l = V2[i].first, r = V2[i].second, x = a[l - 1], y = a[r + 1],
        len = r - l + 1;
    if (MK[i]) {
      a[l] = a[l - 1], a[r] = a[r + 1];
      for (int j = l + 1; j < r; j += 2) a[j] = a[j + 1] = GETNXT();
    } else if (dir[i]) {
      if (dir[i] == x) {
        for (int j = l + 1; j <= r; j += 2) a[j] = a[j + 1] = GETNXT();
        a[l] = a[l - 1];
      } else {
        for (int j = l; j < r; j += 2) a[j] = a[j + 1] = GETNXT();
        a[r] = a[r + 1];
      }
    } else if (len & 1) {
      for (int j = l; j < r; j += 2) a[j] = a[j + 1] = GETNXT();
      a[r] = GETNXT();
    } else {
      for (int j = l; j <= r; j += 2) a[j] = a[j + 1] = GETNXT();
    }
  }
  for (int i = 1; i <= n; i++) printf("%d ", a[i]);
  puts("");
  return 0;
}

### Prompt

Create a solution in CPP for the following problem:

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;
template <typename T>
void read(T &t) {
  t = 0;
  char ch = getchar();
  int f = 1;
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  do {
    (t *= 10) += ch - '0';
    ch = getchar();
  } while ('0' <= ch && ch <= '9');
  t *= f;
}
template <typename T>
void write(T t) {
  if (t < 0) {
    putchar('-');
    write(-t);
    return;
  }
  if (t > 9) write(t / 10);
  putchar('0' + t % 10);
}
template <typename T>
void writeln(T t) {
  write(t);
  puts("");
}
const int maxn = 610;
const int maxm = 300010;
int n, a[maxm];
namespace xyr {
const int maxm = 1000000;
int n, tot, head[maxn], id[610][610];
int nxt[maxm], to[maxm], ans;
void Add(int x, int y) {
  tot++;
  nxt[tot] = head[x];
  head[x] = tot;
  to[tot] = y;
}
void add(int x, int y, int z) {
  if (id[x][y]) return;
  id[x][y] = id[y][x] = z;
  Add(x, y);
  Add(y, x);
}
int match[maxn], pre[maxn], vis[maxn], fa[maxn];
queue<int> q;
int find(int x) {
  if (fa[x] == x) return x;
  return fa[x] = find(fa[x]);
}
int mk[maxn], cnt;
int lca(int x, int y) {
  cnt++;
  while (1) {
    if (x) {
      x = find(x);
      if (mk[x] == cnt) return x;
      mk[x] = cnt;
      x = pre[match[x]];
    }
    swap(x, y);
  }
}
void blossom(int x, int y, int z) {
  while (find(x) != z) {
    pre[x] = y;
    y = match[x];
    if (vis[y] == 2) vis[y] = 1, q.push(y);
    if (find(x) == x) fa[x] = z;
    if (find(y) == y) fa[y] = z;
    x = pre[y];
  }
}
int dfs(int s) {
  for (int i = 1; i <= n; i++) vis[i] = pre[i] = 0, fa[i] = i;
  q = queue<int>();
  q.push(s);
  vis[s] = 1;
  while (!q.empty()) {
    int u = q.front();
    q.pop();
    for (int i = head[u], v; i; i = nxt[i]) {
      v = to[i];
      if (find(u) == find(v) || vis[v] == 2) continue;
      if (!vis[v]) {
        vis[v] = 2;
        pre[v] = u;
        if (!match[v]) {
          for (int x = v, lst; x; x = lst)
            lst = match[pre[x]], match[x] = pre[x], match[pre[x]] = x;
          return 1;
        }
        vis[match[v]] = 1;
        q.push(match[v]);
      } else {
        int z = lca(u, v);
        blossom(u, v, z);
        blossom(v, u, z);
      }
    }
  }
  return 0;
}
void solve() {
  for (int i = n; i >= 1; i--)
    if (!match[i]) ans += dfs(i);
}
};  // namespace xyr
bool ban[610];
int mx, used[maxm];
vector<pair<int, int>> V, V2;
namespace BF {
vector<int> g[610];
int tim[610];
queue<int> q;
void link(int x, int y) { g[x].push_back(y), g[y].push_back(x); }
void solve() {
  for (int i = 1; i <= mx; i++) tim[i] = -1;
  for (int i = 1; i <= mx; i++)
    if (ban[i]) tim[i] = 0, q.push(i);
  while (!q.empty()) {
    int x = q.front();
    q.pop();
    for (int &y : g[x])
      if (tim[y] == -1) tim[y] = tim[x] + 1, q.push(y);
  }
}
};  // namespace BF
int dir[maxm], bel[maxn];
bool MK[maxm];
namespace Forest {
bool oncyc[610], vis[610];
int fa[610], from[610];
vector<pair<int, int>> g[610];
void add(int x, int y, int z) {
  g[x].push_back(make_pair(y, z)), g[y].push_back(make_pair(x, z));
}
int X, Y, Z;
vector<int> V[610];
int D[610], tot, S, dis[610];
void dfs(int x, int p, int w) {
  vis[x] = 1;
  fa[x] = p;
  from[x] = w;
  V[S].push_back(x);
  dis[x] = dis[p] + 1;
  for (auto [y, z] : g[x]) {
    if (z == from[x]) continue;
    if (vis[y]) {
      if (dis[x] > dis[y]) Y = x, X = y, Z = z;
    } else
      dfs(y, x, z);
  }
}
int VIS[610];
void DFS(int x, int f) {
  VIS[x] = 1;
  for (auto [y, z] : g[x])
    if (!oncyc[y] && z != f && !VIS[y]) {
      DFS(y, z);
      dir[z] = y;
    }
}
int TREE[610];
void solve() {
  for (int i = 1; i <= mx; i++)
    if (!vis[i]) {
      X = Y = 0;
      S = i;
      dfs(i, 0, -1);
      if (X) {
        tot = 0;
        dir[Z] = X;
        while (1) {
          D[++tot] = Y;
          if (Y == X) break;
          dir[from[Y]] = Y;
          Y = fa[Y];
        }
        for (int j = 1; j <= tot; j++) oncyc[D[j]] = 1;
        for (int j = 1; j <= tot; j++) DFS(D[j], 0);
      } else {
        TREE[i] = 1;
        for (int &x : V[i]) {
          bel[x] = i;
        }
      }
    }
  tot = 0;
}
int XYR[610];
void insert(int x) { XYR[bel[x]] = x; }
void insert(int x, int y) { insert(x), insert(y); }
void solve_again() {
  memset(vis, 0, sizeof(vis));
  for (int i = 1; i <= mx; i++)
    if (bel[i] == i && TREE[i]) {
      if (XYR[i]) {
        S = i;
        V[i].clear();
        dfs(XYR[i], 0, -1);
      } else
        XYR[i] = i;
      for (int &x : V[i])
        if (x != XYR[i]) dir[from[x]] = x;
    }
}
};  // namespace Forest
int now, R[maxm];
int GETNXT() {
  while (used[now]) now++;
  used[now] = 1;
  return now;
}
int main() {
  read(n);
  int F1 = 1, F2 = 1;
  for (int i = 1; i <= n; i++)
    read(a[i]), R[i] = a[i], mx = max(mx, a[i]), used[a[i]] = 1,
                F1 &= (a[i] == 0), F2 &= (a[i] != 0);
  if (F1) {
    for (int i = 0; i < n; i++) printf("%d ", i / 2 + 1);
    puts("");
    return 0;
  }
  if (F2) {
    for (int i = 1; i <= n; i++) printf("%d ", a[i]);
    puts("");
    return 0;
  }
  now = 1;
  for (int l = 1, r; l <= n; l = r + 1)
    if (!a[l]) {
      r = l;
      while (r < n && !a[r + 1]) r++;
      int x = a[l - 1], y = a[r + 1], len = r - l + 1;
      if (l == 1) {
        if (len & 1) {
          for (int i = 1; i < r; i += 2) a[i] = a[i + 1] = GETNXT();
          a[r] = a[r + 1];
        } else {
          for (int i = 1; i <= r; i += 2) a[i] = a[i + 1] = GETNXT();
        }
      } else if (r == n) {
        if (len & 1) {
          for (int i = l + 1; i <= n; i += 2) a[i] = a[i + 1] = GETNXT();
          a[l] = a[l - 1];
        } else {
          for (int i = l; i <= n; i += 2) a[i] = a[i + 1] = GETNXT();
        }
      } else {
        assert(x && y);
        if (x == y) {
          if (len & 1) {
            a[l] = a[l - 1];
            for (int i = l + 1; i <= r; i += 2) a[i] = a[i + 1] = GETNXT();
          } else {
            for (int i = l; i <= r; i += 2) a[i] = a[i + 1] = GETNXT();
          }
        } else {
          V.push_back(make_pair(l, r));
        }
      }
    } else
      r = l;
  for (int i = 1; i < n; i++)
    if (a[i] && a[i + 1] && a[i] == a[i + 1] && a[i] <= mx) ban[a[i]] = 1;
  for (pair<int, int> &A : V)
    if ((A.second - A.first + 1) % 2 == 1)
      BF::link(a[A.first - 1], a[A.second + 1]);
  BF::solve();
  for (int i = 1; i <= mx; i++) ban[i] = (BF::tim[i] != -1);
  for (auto [l, r] : V) {
    int x = a[l - 1], y = a[r + 1], len = r - l + 1;
    if (ban[y] && (!ban[x] || BF::tim[y] <= BF::tim[x])) {
      if (len & 1) {
        for (int i = l + 1; i <= r; i += 2) a[i] = a[i + 1] = GETNXT();
        a[l] = a[l - 1];
      } else {
        for (int i = l; i <= r; i += 2) a[i] = a[i + 1] = GETNXT();
      }
    } else if (ban[x] && (!ban[y] || BF::tim[y] >= BF::tim[x])) {
      if (len & 1) {
        for (int i = l; i < r; i += 2) a[i] = a[i + 1] = GETNXT();
        a[r] = a[r + 1];
      } else {
        for (int i = l; i <= r; i += 2) a[i] = a[i + 1] = GETNXT();
      }
    } else
      V2.push_back(make_pair(l, r));
  }
  for (int i = 0; i < V2.size(); i++) {
    int l = V2[i].first, r = V2[i].second, x = a[l - 1], y = a[r + 1],
        len = r - l + 1;
    if (len & 1) Forest::add(x, y, i);
  }
  Forest::solve();
  xyr::n = mx;
  for (int i = 0; i < V2.size(); i++) {
    int l = V2[i].first, r = V2[i].second, x = a[l - 1], y = a[r + 1],
        len = r - l + 1;
    if (len & 1 ^ 1) xyr::add(bel[x], bel[y], i + 1);
  }
  xyr::solve();
  for (int i = 1; i <= mx; i++)
    if (xyr::match[i] && xyr::match[i] < i) {
      int z = xyr::id[i][xyr::match[i]] - 1;
      MK[z] = 1;
      int x = a[V2[z].first - 1], y = a[V2[z].second + 1];
      Forest::insert(x, y);
    }
  Forest::solve_again();
  for (int i = 0; i < V2.size(); i++) {
    int l = V2[i].first, r = V2[i].second, x = a[l - 1], y = a[r + 1],
        len = r - l + 1;
    if (MK[i]) {
      a[l] = a[l - 1], a[r] = a[r + 1];
      for (int j = l + 1; j < r; j += 2) a[j] = a[j + 1] = GETNXT();
    } else if (dir[i]) {
      if (dir[i] == x) {
        for (int j = l + 1; j <= r; j += 2) a[j] = a[j + 1] = GETNXT();
        a[l] = a[l - 1];
      } else {
        for (int j = l; j < r; j += 2) a[j] = a[j + 1] = GETNXT();
        a[r] = a[r + 1];
      }
    } else if (len & 1) {
      for (int j = l; j < r; j += 2) a[j] = a[j + 1] = GETNXT();
      a[r] = GETNXT();
    } else {
      for (int j = l; j <= r; j += 2) a[j] = a[j + 1] = GETNXT();
    }
  }
  for (int i = 1; i <= n; i++) printf("%d ", a[i]);
  puts("");
  return 0;
}

```