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:
from collections import Counter
import sys
def muri():
    print(-1)
    sys.exit()
N = int(input())
D = [int(sys.stdin.readline()) for _ in range(N)]
#D = list(map(int, input().split()))
Didx = list(range(1, N+1))
Didx.sort(key = lambda x: -D[x-1])
H = {d: i for i, d in enumerate(D, 1)}
H = Counter(H)
D = [0] + D
K = [1]*(N+1)
Ans = []
for vn in Didx[:-1]:
    p = H[D[vn] - (N - 2*K[vn])]
    if not p:
        muri()
    Ans.append((vn, p))
    K[p] += K[vn]
s = set()

Edge = [[] for _ in range(N+1)]
for a in Ans:
    x, y = a
    Edge[x].append(y)
    Edge[y].append(x)

dist = [10**9+7]*(N+1)
dist[0] = 0
dist[1] = 0
stack = [1]
visited = set([1])
while stack:
    vn = stack.pop()
    for vf in Edge[vn]:
        if vf not in visited:
            visited.add(vf)
            dist[vf] = 1 + dist[vn]
            stack.append(vf)
if D[1] != sum(dist[1:]):
    muri()

for a in Ans:
    print(*a)