Problem: You are given a sequence D_1, D_2, ..., D_N of length N. The values of D_i are all distinct. Does a tree with N vertices that satisfies the following conditions exist?

* The vertices are numbered 1,2,..., N.
* The edges are numbered 1,2,..., N-1, and Edge i connects Vertex u_i and v_i.
* For each vertex i, the sum of the distances from i to the other vertices is D_i, assuming that the length of each edge is 1.



If such a tree exists, construct one such tree.

Constraints

* 2 \leq N \leq 100000
* 1 \leq D_i \leq 10^{12}
* D_i are all distinct.

Input

Input is given from Standard Input in the following format:


N
D_1
D_2
:
D_N


Output

If a tree with n vertices that satisfies the conditions does not exist, print `-1`.

If a tree with n vertices that satisfies the conditions exist, print n-1 lines. The i-th line should contain u_i and v_i with a space in between. If there are multiple trees that satisfy the conditions, any such tree will be accepted.

Examples

Input

7
10
15
13
18
11
14
19


Output

1 2
1 3
1 5
3 4
5 6
6 7


Input

2
1
2


Output

-1


Input

15
57
62
47
45
42
74
90
75
54
50
66
63
77
87
51


Output

1 10
1 11
2 8
2 15
3 5
3 9
4 5
4 10
5 15
6 12
6 14
7 13
9 12
11 13

Solution (in CPP):

Solution:
#include <algorithm>
#include <cstdio>
#include <cstring>

#define int long long
#define Accepted 0; 

const int Maxv = 100010; 
int d[Maxv], d1[Maxv], u[Maxv], ghostfly233[Maxv], siz[Maxv], cnt, n;  

inline int GldHkkowoSearch(int x) {
    int tmp = std::lower_bound(d + 1, d + n + 1, x) - d;

    if (d[tmp] != x) {
        puts("-1"); 
        exit(0); 
    }

    return tmp; 
}

signed main() {
    scanf("%lld", &n); 
    for (int i = 1; i <= n; i++) {
        scanf("%lld", &d[i]); 
        d1[i] = d[i]; 
    }

    std::sort(d + 1, d + n + 1); 
    for (int i = 1; i <= n; i++) 
        ghostfly233[GldHkkowoSearch(d1[i])] = i;       

    for (int i = 1; i <= n; i++)
        siz[i] = 1; 

    for (int i = n; i > 1; i--) {
        u[i] = GldHkkowoSearch(d[i] - n + (siz[i] << 1)); 
        siz[ u[i] ] += siz[i]; 
        cnt += siz[i]; 
    }

    if (cnt != d[1]) {
        puts("-1"); 
        return 0; 
    }

    for (int i = 2; i <= n; i++)
        printf("%lld %lld\n", ghostfly233[i], ghostfly233[ u[i] ]); 

    return Accepted;  
}