#include <bits/stdc++.h>
using namespace std;
long long q[500005], p[500005], pp[500005];
int main() {
  set<long long> s;
  long long n;
  cin >> n;
  long long pos = 0;
  long long minn = 999999999999999999;
  long long sum = 0;
  for (long long i = 0; i < n - 1; i++) {
    scanf("%lld", &q[i]);
    sum += q[i];
    if (sum <= minn && q[i] < 0) {
      pos = i + 1;
      minn = sum;
    }
  }
  p[pos] = 1;
  for (long long i = pos - 1; i >= 0; i--) {
    p[i] = p[i + 1] - q[i];
  }
  for (long long i = pos + 1; i < n; i++) {
    p[i] = p[i - 1] + q[i - 1];
  }
  for (long long i = 0; i < n; i++) {
    pp[i] = p[i];
  }
  sort(pp, pp + n);
  for (long long i = 1; i < n; i++) {
    if (pp[i] - pp[i - 1] != 1) {
      printf("-1\n");
      return 0;
    }
  }
  int d = 0;
  if (pp[0] != -1) d = pp[0] - 1;
  for (long long i = 0; i < n; i++) cout << p[i] - d << " ";
}

### Prompt

Please formulate a CPP solution to 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>
using namespace std;
long long q[500005], p[500005], pp[500005];
int main() {
  set<long long> s;
  long long n;
  cin >> n;
  long long pos = 0;
  long long minn = 999999999999999999;
  long long sum = 0;
  for (long long i = 0; i < n - 1; i++) {
    scanf("%lld", &q[i]);
    sum += q[i];
    if (sum <= minn && q[i] < 0) {
      pos = i + 1;
      minn = sum;
    }
  }
  p[pos] = 1;
  for (long long i = pos - 1; i >= 0; i--) {
    p[i] = p[i + 1] - q[i];
  }
  for (long long i = pos + 1; i < n; i++) {
    p[i] = p[i - 1] + q[i - 1];
  }
  for (long long i = 0; i < n; i++) {
    pp[i] = p[i];
  }
  sort(pp, pp + n);
  for (long long i = 1; i < n; i++) {
    if (pp[i] - pp[i - 1] != 1) {
      printf("-1\n");
      return 0;
    }
  }
  int d = 0;
  if (pp[0] != -1) d = pp[0] - 1;
  for (long long i = 0; i < n; i++) cout << p[i] - d << " ";
}

```