#include <bits/stdc++.h>
const int mod = 1e9 + 7, MAX = 2e5 + 5;
const long long inf = 1e18;
const double eps = 1e-9;
using namespace std;
struct abc {
  char a;
  int i;
};
bool comp(abc a, abc b) { return a.a > b.a; }
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  vector<long long> q(n - 1);
  for (int i = 0; i < n - 1; ++i) cin >> q[i];
  vector<long long> ans(n);
  ans[0] = 0;
  for (int i = 1; i < n; i++) {
    ans[i] = q[i - 1] + ans[i - 1];
  }
  long long mini = 1e18;
  for (int i = 0; i < n; ++i) mini = min(mini, (long long)ans[i]);
  mini--;
  for (int i = 0; i < n; ++i) ans[i] -= mini;
  set<int> a;
  for (int i = 0; i < n; ++i) {
    if (a.count(ans[i]) || ans[i] > n) {
      cout << -1;
      return 0;
    }
    a.insert(ans[i]);
  }
  for (int i = 0; i < n; ++i) cout << ans[i] << ' ';
}

### Prompt

In Cpp, your task is to solve the following problem:

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>
const int mod = 1e9 + 7, MAX = 2e5 + 5;
const long long inf = 1e18;
const double eps = 1e-9;
using namespace std;
struct abc {
  char a;
  int i;
};
bool comp(abc a, abc b) { return a.a > b.a; }
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  vector<long long> q(n - 1);
  for (int i = 0; i < n - 1; ++i) cin >> q[i];
  vector<long long> ans(n);
  ans[0] = 0;
  for (int i = 1; i < n; i++) {
    ans[i] = q[i - 1] + ans[i - 1];
  }
  long long mini = 1e18;
  for (int i = 0; i < n; ++i) mini = min(mini, (long long)ans[i]);
  mini--;
  for (int i = 0; i < n; ++i) ans[i] -= mini;
  set<int> a;
  for (int i = 0; i < n; ++i) {
    if (a.count(ans[i]) || ans[i] > n) {
      cout << -1;
      return 0;
    }
    a.insert(ans[i]);
  }
  for (int i = 0; i < n; ++i) cout << ans[i] << ' ';
}

```