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
from bisect import bisect_left
def input():
	return sys.stdin.readline()[:-1]
sys.setrecursionlimit(10**6)

n = int(input())
d = [[int(input()), i+1] for i in range(n)]
check = d[0][0]
d.sort()
ind = [x[1] for x in d]
d = [x[0] for x in d]
if n <= 3:
	print(-1)
	sys.exit()
#print(d)
child = [1 for _ in range(n)]
#print(gap)
ans = []
adj = [[] for _ in range(n)]
for i in range(n-1, 0, -1):
	x = d[i]
	b = bisect_left(d, x - n + 2*child[i])
	#print(i, x, n - 2+child[i], b)
	if d[b] != x - n + 2*child[i] or n <= 2*child[i]:
		print(-1)
		sys.exit()
	else:
		child[b] += child[i]
		ans.append([ind[b], ind[i]])
		adj[ind[b]-1].append(ind[i]-1)
		adj[ind[i]-1].append(ind[b]-1)


res = 0
def dfs(x, p, dis):
	global res
	res += dis
	for v in adj[x]:
		if v == p:
			continue
		else:
			dfs(v, x, dis+1)
	return

dfs(0, -1, 0)
if res == check:
	for a in ans:
		print(*a)
else:
	print(-1)