Problem: Mike has discovered a new way to encode permutations. If he has a permutation P = [p1, p2, ..., pn], he will encode it in the following way:

Denote by A = [a1, a2, ..., an] a sequence of length n which will represent the code of the permutation. For each i from 1 to n sequentially, he will choose the smallest unmarked j (1 ≤ j ≤ n) such that pi < pj and will assign to ai the number j (in other words he performs ai = j) and will mark j. If there is no such j, he'll assign to ai the number  - 1 (he performs ai = - 1). 

Mike forgot his original permutation but he remembers its code. Your task is simple: find any permutation such that its code is the same as the code of Mike's original permutation.

You may assume that there will always be at least one valid permutation.

Input

The first line contains single integer n (1 ≤ n ≤ 500 000) — length of permutation.

The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ n or ai = - 1) — the code of Mike's permutation.

You may assume that all positive values from A are different.

Output

In first and only line print n numbers p1, p2, ..., pn (1 ≤ pi ≤ n) — a permutation P which has the same code as the given one. Note that numbers in permutation are distinct.

Examples

Input

6
2 -1 1 5 -1 4


Output

2 6 1 4 5 3


Input

8
2 -1 4 -1 6 -1 8 -1


Output

1 8 2 7 3 6 4 5

Note

For the permutation from the first example:

i = 1, the smallest j is 2 because p2 = 6 > p1 = 2.

i = 2, there is no j because p2 = 6 is the greatest element in the permutation.

i = 3, the smallest j is 1 because p1 = 2 > p3 = 1.

i = 4, the smallest j is 5 (2 was already marked) because p5 = 5 > p4 = 4.

i = 5, there is no j because 2 is already marked.

i = 6, the smallest j is 4 because p4 = 4 > p6 = 3.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int MOD = 1e9 + 7;
const int MX = 1 << 19;
const long long INF = 1e18;
const long double PI = acos((long double)-1);
const int xd[4] = {1, 0, -1, 0}, yd[4] = {0, 1, 0, -1};
template <class T>
bool ckmin(T& a, const T& b) {
  return b < a ? a = b, 1 : 0;
}
template <class T>
bool ckmax(T& a, const T& b) {
  return a < b ? a = b, 1 : 0;
}
int pct(int x) { return __builtin_popcount(x); }
namespace input {
template <class T>
void re(complex<T>& x);
template <class T1, class T2>
void re(pair<T1, T2>& p);
template <class T>
void re(vector<T>& a);
template <class T, size_t SZ>
void re(array<T, SZ>& a);
template <class T>
void re(T& x) {
  cin >> x;
}
void re(double& x) {
  string t;
  re(t);
  x = stod(t);
}
void re(long double& x) {
  string t;
  re(t);
  x = stold(t);
}
template <class T, class... Ts>
void re(T& t, Ts&... ts) {
  re(t);
  re(ts...);
}
template <class T>
void re(complex<T>& x) {
  T a, b;
  re(a, b);
  x = {a, b};
}
template <class T1, class T2>
void re(pair<T1, T2>& p) {
  re(p.first, p.second);
}
template <class T>
void re(vector<T>& a) {
  for (int i = (0); i < ((int)a.size()); ++i) re(a[i]);
}
template <class T, size_t SZ>
void re(array<T, SZ>& a) {
  for (int i = (0); i < (SZ); ++i) re(a[i]);
}
}  // namespace input
using namespace input;
namespace output {
void pr(int x) { cout << x; }
void pr(long x) { cout << x; }
void pr(long long x) { cout << x; }
void pr(unsigned x) { cout << x; }
void pr(unsigned long x) { cout << x; }
void pr(unsigned long long x) { cout << x; }
void pr(float x) { cout << x; }
void pr(double x) { cout << x; }
void pr(long double x) { cout << x; }
void pr(char x) { cout << x; }
void pr(const char* x) { cout << x; }
void pr(const string& x) { cout << x; }
void pr(bool x) { pr(x ? "true" : "false"); }
template <class T>
void pr(const complex<T>& x) {
  cout << x;
}
template <class T1, class T2>
void pr(const pair<T1, T2>& x);
template <class T>
void pr(const T& x);
template <class T, class... Ts>
void pr(const T& t, const Ts&... ts) {
  pr(t);
  pr(ts...);
}
template <class T1, class T2>
void pr(const pair<T1, T2>& x) {
  pr("{", x.first, ", ", x.second, "}");
}
template <class T>
void pr(const T& x) {
  pr("{");
  bool fst = 1;
  for (const auto& a : x) pr(!fst ? ", " : "", a), fst = 0;
  pr("}");
}
void ps() { pr("\n"); }
template <class T, class... Ts>
void ps(const T& t, const Ts&... ts) {
  pr(t);
  if (sizeof...(ts)) pr(" ");
  ps(ts...);
}
void pc() { pr("]\n"); }
template <class T, class... Ts>
void pc(const T& t, const Ts&... ts) {
  pr(t);
  if (sizeof...(ts)) pr(", ");
  pc(ts...);
}
}  // namespace output
using namespace output;
namespace io {
void setIn(string second) { freopen(second.c_str(), "r", stdin); }
void setOut(string second) { freopen(second.c_str(), "w", stdout); }
void setIO(string second = "") {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  if ((int)second.size()) {
    setIn(second + ".in"), setOut(second + ".out");
  }
}
}  // namespace io
using namespace io;
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
int n, a[MX], mark[MX], val[MX];
bool vis[MX];
vector<int> ans;
int seg[2 * MX];
int bet(int a, int b) { return mark[a] > mark[b] ? a : b; }
int query(int r) {
  int l = (1 << 19), ans = 0;
  r += (1 << 19) + 1;
  for (; l < r; l /= 2, r /= 2)
    if (r & 1) ans = bet(ans, seg[--r]);
  return ans;
}
void insert(int x, int d) {
  int ind = x + (1 << 19);
  seg[ind] = (d == 1 ? x : 0);
  for (ind /= 2; ind; ind /= 2) seg[ind] = bet(seg[2 * ind], seg[2 * ind + 1]);
}
void dfs(int x) {
  if (vis[x]) return;
  vis[x] = 1;
  insert(x, -1);
  if (mark[x] != n + 1) dfs(mark[x]);
  while (1) {
    int t = query(a[x] - 1);
    if (mark[t] <= x) break;
    dfs(t);
  }
  ans.push_back(x);
}
int main() {
  setIO();
  re(n);
  for (int i = (1); i < (n + 1); ++i) mark[i] = n + 1;
  for (int i = (1); i < (n + 1); ++i) {
    re(a[i]);
    if (a[i] == -1) a[i] = n + 1;
    if (a[i] != n + 1) mark[a[i]] = i;
  }
  for (int i = (1); i < (n + 1); ++i) insert(i, 1);
  for (int i = (1); i < (n + 1); ++i)
    if (!vis[i]) dfs(i);
  for (int i = (0); i < ((int)ans.size()); ++i) val[ans[i]] = i + 1;
  for (int i = (1); i < (n + 1); ++i) pr(val[i], ' ');
}