#include <bits/stdc++.h>
using namespace std;
const int INF = 1e9;
const int N = 1e5;
const int MOD = 1e9 + 7;
const double PI = acos(-1);
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0), cout.tie(0);
  int n;
  cin >> n;
  int q[n - 1];
  for (int& x : q) cin >> x;
  int cur = 0;
  for (int& x : q) {
    cur += x;
    x = cur;
  }
  bool allNeg = 1, allPos = 1;
  int mx = *max_element(q, q + n - 1);
  for (int x : q) {
    if (x < 0) allPos = 0;
    if (x > 0) allNeg = 0;
  }
  int k;
  if (allNeg)
    k = n;
  else if (allPos)
    k = 1;
  else
    k = n - mx;
  vector<int> res, chk;
  res.push_back(k);
  chk.push_back(k);
  for (int x : q) {
    res.push_back(k + x);
    chk.push_back(k + x);
  }
  sort(chk.begin(), chk.end());
  for (int i = 1; i <= n; i++) {
    if (chk[i - 1] != i) {
      cout << -1;
      exit(0);
    }
  }
  for (int x : res) cout << x << ' ';
}

### Prompt

Construct a CPP code solution to the problem outlined:

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].

Polycarp invented a really cool permutation p_1, p_2, ..., p_n of length n. It is very disappointing, but he forgot this permutation. He only remembers the array q_1, q_2, ..., q_{n-1} of length n-1, where q_i=p_{i+1}-p_i.

Given n and q=q_1, q_2, ..., q_{n-1}, help Polycarp restore the invented permutation.

Input

The first line contains the integer n (2 ≤ n ≤ 2⋅10^5) — the length of the permutation to restore. The second line contains n-1 integers q_1, q_2, ..., q_{n-1} (-n < q_i < n).

Output

Print the integer -1 if there is no such permutation of length n which corresponds to the given array q. Otherwise, if it exists, print p_1, p_2, ..., p_n. Print any such permutation if there are many of them.

Examples

Input


3
-2 1


Output


3 1 2 

Input


5
1 1 1 1


Output


1 2 3 4 5 

Input


4
-1 2 2


Output


-1

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int INF = 1e9;
const int N = 1e5;
const int MOD = 1e9 + 7;
const double PI = acos(-1);
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0), cout.tie(0);
  int n;
  cin >> n;
  int q[n - 1];
  for (int& x : q) cin >> x;
  int cur = 0;
  for (int& x : q) {
    cur += x;
    x = cur;
  }
  bool allNeg = 1, allPos = 1;
  int mx = *max_element(q, q + n - 1);
  for (int x : q) {
    if (x < 0) allPos = 0;
    if (x > 0) allNeg = 0;
  }
  int k;
  if (allNeg)
    k = n;
  else if (allPos)
    k = 1;
  else
    k = n - mx;
  vector<int> res, chk;
  res.push_back(k);
  chk.push_back(k);
  for (int x : q) {
    res.push_back(k + x);
    chk.push_back(k + x);
  }
  sort(chk.begin(), chk.end());
  for (int i = 1; i <= n; i++) {
    if (chk[i - 1] != i) {
      cout << -1;
      exit(0);
    }
  }
  for (int x : res) cout << x << ' ';
}

```