#include <bits/stdc++.h>
using namespace std;
int f(int a, int b) {
  int total = 0;
  while (a % b == 0) {
    total++;
    a = a / b;
  }
  return total;
}
int main() {
  int test;
  test = 1;
  while (test--) {
    int n;
    cin >> n;
    int arr[n];
    arr[0] = 0;
    int mini = 0, temp;
    for (int i = 1; i < n; i++) {
      cin >> temp;
      arr[i] = arr[i - 1] + temp;
      mini = min(mini, arr[i]);
    }
    for (int i = 0; i < n; i++) {
      arr[i] = arr[i] + (1 - mini);
    }
    int fl = true;
    int flag[n + 1];
    for (int i = 0; i <= n; i++) flag[i] = false;
    for (int i = 0; i < n; i++) {
      if (arr[i] >= 1 && arr[i] <= n) {
        flag[arr[i]] = true;
        continue;
      }
      fl = false;
      break;
    }
    for (int i = 1; i <= n; i++) {
      if (flag[i] == false) {
        fl = false;
        break;
      }
    }
    if (fl) {
      for (int i = 0; i < n; i++) {
        cout << arr[i] << " ";
      }
    } else
      cout << -1;
  }
}

### Prompt

Develop a solution in CPP 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].

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;
int f(int a, int b) {
  int total = 0;
  while (a % b == 0) {
    total++;
    a = a / b;
  }
  return total;
}
int main() {
  int test;
  test = 1;
  while (test--) {
    int n;
    cin >> n;
    int arr[n];
    arr[0] = 0;
    int mini = 0, temp;
    for (int i = 1; i < n; i++) {
      cin >> temp;
      arr[i] = arr[i - 1] + temp;
      mini = min(mini, arr[i]);
    }
    for (int i = 0; i < n; i++) {
      arr[i] = arr[i] + (1 - mini);
    }
    int fl = true;
    int flag[n + 1];
    for (int i = 0; i <= n; i++) flag[i] = false;
    for (int i = 0; i < n; i++) {
      if (arr[i] >= 1 && arr[i] <= n) {
        flag[arr[i]] = true;
        continue;
      }
      fl = false;
      break;
    }
    for (int i = 1; i <= n; i++) {
      if (flag[i] == false) {
        fl = false;
        break;
      }
    }
    if (fl) {
      for (int i = 0; i < n; i++) {
        cout << arr[i] << " ";
      }
    } else
      cout << -1;
  }
}

```