#include <bits/stdc++.h>
const int N = 1e6 + 10;
const long long int INF = 1e18;
const int MOD = 998244353;
const int lgN = 20;
using namespace std;
long long int tree[4 * N], lz[4 * N], v[N], w[N];
void build(int node, int st, int en) {
  lz[node] = 0;
  if (st == en) {
    tree[node] = v[st];
    return;
  }
  int m = (st + en) / 2;
  build(2 * node + 1, st, m);
  build(2 * node + 2, m + 1, en);
  tree[node] = min(tree[2 * node + 1], tree[2 * node + 2]);
}
void pushdown(int node, int st, int en) {
  if (lz[node] > 0) {
    tree[node] -= lz[node];
    if (st < en) {
      lz[2 * node + 1] += lz[node];
      lz[2 * node + 2] += lz[node];
    }
    lz[node] = 0;
  }
}
void pupd(int pos, long long int val, int node, int st, int en) {
  pushdown(node, st, en);
  if (st == en) {
    tree[node] = val;
    return;
  }
  int m = (st + en) / 2;
  pushdown(2 * node + 1, st, m);
  pushdown(2 * node + 2, m + 1, en);
  if (pos <= m)
    pupd(pos, val, 2 * node + 1, st, m);
  else
    pupd(pos, val, 2 * node + 2, m + 1, en);
  tree[node] = min(tree[2 * node + 1], tree[2 * node + 2]);
}
void upd(int l, int r, int val, int node, int st, int en) {
  pushdown(node, st, en);
  if (st > r || en < l) return;
  int m = (st + en) / 2;
  if (st >= l && en <= r) {
    tree[node] -= val;
    if (st < en) {
      lz[2 * node + 1] += val;
      lz[2 * node + 2] += val;
    }
    return;
  }
  upd(l, r, val, 2 * node + 1, st, m);
  upd(l, r, val, 2 * node + 2, m + 1, en);
  tree[node] = min(tree[2 * node + 1], tree[2 * node + 2]);
}
int query(int node, int st, int en) {
  pushdown(node, st, en);
  if (st == en) return st;
  int m = (st + en) / 2;
  pushdown(2 * node + 1, st, m);
  pushdown(2 * node + 2, m + 1, en);
  if (tree[2 * node + 2] <= tree[2 * node + 1])
    return query(2 * node + 2, m + 1, en);
  return query(2 * node + 1, st, m);
}
void solve() {
  int n, i, go = 1;
  cin >> n;
  for (i = 0; i < n; i++) cin >> v[i];
  build(0, 0, n - 1);
  while (go <= n) {
    int ans = query(0, 0, n - 1);
    assert(ans >= 0 && ans <= n - 1);
    w[ans] = go;
    if (ans + 1 < n) upd(ans + 1, n - 1, go, 0, 0, n - 1);
    go++;
    pupd(ans, INF, 0, 0, n - 1);
  }
  for (i = 0; i < n; i++) cout << w[i] << " \n"[i == n - 1];
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  int T = 1;
  for (int t = 1; t <= T; t++) {
    solve();
  }
  return 0;
}

### Prompt

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

An array of integers p_{1},p_{2}, …,p_{n} is called a permutation if it contains each number from 1 to n exactly once. For example, the following arrays are permutations: [3,1,2], [1], [1,2,3,4,5] and [4,3,1,2]. The following arrays are not permutations: [2], [1,1], [2,3,4].

There is a hidden permutation of length n.

For each index i, you are given s_{i}, which equals to the sum of all p_{j} such that j < i and p_{j} < p_{i}. In other words, s_i is the sum of elements before the i-th element that are smaller than the i-th element.

Your task is to restore the permutation.

Input

The first line contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^{5}) — the size of the permutation.

The second line contains n integers s_{1}, s_{2}, …, s_{n} (0 ≤ s_{i} ≤ (n(n-1))/(2)).

It is guaranteed that the array s corresponds to a valid permutation of length n.

Output

Print n integers p_{1}, p_{2}, …, p_{n} — the elements of the restored permutation. We can show that the answer is always unique.

Examples

Input


3
0 0 0


Output


3 2 1


Input


2
0 1


Output


1 2


Input


5
0 1 1 1 10


Output


1 4 3 2 5

Note

In the first example for each i there is no index j satisfying both conditions, hence s_i are always 0.

In the second example for i = 2 it happens that j = 1 satisfies the conditions, so s_2 = p_1.

In the third example for i = 2, 3, 4 only j = 1 satisfies the conditions, so s_2 = s_3 = s_4 = 1. For i = 5 all j = 1, 2, 3, 4 are possible, so s_5 = p_1 + p_2 + p_3 + p_4 = 10.

### Response

```cpp
#include <bits/stdc++.h>
const int N = 1e6 + 10;
const long long int INF = 1e18;
const int MOD = 998244353;
const int lgN = 20;
using namespace std;
long long int tree[4 * N], lz[4 * N], v[N], w[N];
void build(int node, int st, int en) {
  lz[node] = 0;
  if (st == en) {
    tree[node] = v[st];
    return;
  }
  int m = (st + en) / 2;
  build(2 * node + 1, st, m);
  build(2 * node + 2, m + 1, en);
  tree[node] = min(tree[2 * node + 1], tree[2 * node + 2]);
}
void pushdown(int node, int st, int en) {
  if (lz[node] > 0) {
    tree[node] -= lz[node];
    if (st < en) {
      lz[2 * node + 1] += lz[node];
      lz[2 * node + 2] += lz[node];
    }
    lz[node] = 0;
  }
}
void pupd(int pos, long long int val, int node, int st, int en) {
  pushdown(node, st, en);
  if (st == en) {
    tree[node] = val;
    return;
  }
  int m = (st + en) / 2;
  pushdown(2 * node + 1, st, m);
  pushdown(2 * node + 2, m + 1, en);
  if (pos <= m)
    pupd(pos, val, 2 * node + 1, st, m);
  else
    pupd(pos, val, 2 * node + 2, m + 1, en);
  tree[node] = min(tree[2 * node + 1], tree[2 * node + 2]);
}
void upd(int l, int r, int val, int node, int st, int en) {
  pushdown(node, st, en);
  if (st > r || en < l) return;
  int m = (st + en) / 2;
  if (st >= l && en <= r) {
    tree[node] -= val;
    if (st < en) {
      lz[2 * node + 1] += val;
      lz[2 * node + 2] += val;
    }
    return;
  }
  upd(l, r, val, 2 * node + 1, st, m);
  upd(l, r, val, 2 * node + 2, m + 1, en);
  tree[node] = min(tree[2 * node + 1], tree[2 * node + 2]);
}
int query(int node, int st, int en) {
  pushdown(node, st, en);
  if (st == en) return st;
  int m = (st + en) / 2;
  pushdown(2 * node + 1, st, m);
  pushdown(2 * node + 2, m + 1, en);
  if (tree[2 * node + 2] <= tree[2 * node + 1])
    return query(2 * node + 2, m + 1, en);
  return query(2 * node + 1, st, m);
}
void solve() {
  int n, i, go = 1;
  cin >> n;
  for (i = 0; i < n; i++) cin >> v[i];
  build(0, 0, n - 1);
  while (go <= n) {
    int ans = query(0, 0, n - 1);
    assert(ans >= 0 && ans <= n - 1);
    w[ans] = go;
    if (ans + 1 < n) upd(ans + 1, n - 1, go, 0, 0, n - 1);
    go++;
    pupd(ans, INF, 0, 0, n - 1);
  }
  for (i = 0; i < n; i++) cout << w[i] << " \n"[i == n - 1];
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  int T = 1;
  for (int t = 1; t <= T; t++) {
    solve();
  }
  return 0;
}

```