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 PYTHON3):

Solution:
import sys
sys.setrecursionlimit(10**7)
n = int(input())
d = [int(input()) for _ in range(n)]
r = {v: i for i, v in enumerate(d)}
sz = [1] * n
dsorted = sorted(((di, i) for i, di in enumerate(d)), reverse=True)
ans = []
to = [[] for _ in range(n)]
for di, i in dsorted[:n-1]:
    nd = di + (sz[i] - 1) - (n - 2 - (sz[i] - 1))
    if not nd in r:
        print(-1)
        exit()
    p = r[nd]
    to[p].append(i)
    sz[p] += sz[i]
    ans.append((i+1, p+1))

root = dsorted[-1][1]
def dfs(u, cur=0):
    rv = cur
    for v in to[u]:
        rv += dfs(v, cur + 1)
    return rv

if dfs(root) != d[root]:
    print(-1)
    exit()

for u, v in ans:
    print(u, v)