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.

-----Sample Input-----
7
10
15
13
18
11
14
19

-----Sample Output-----
1 2
1 3
1 5
3 4
5 6
6 7

The tree shown below satisfies the conditions.

Difficulty: VERY_HARD

Solutions:
import sys
sys.setrecursionlimit(101010)

def dfs(v, adj_list, depth, visited):
	visited[v] = True
	x = depth
	for w in adj_list[v]:
		if not visited[w]:
			x += dfs(w, adj_list, depth + 1, visited)
	return x

def solve(n, d):
	if n < 7:
		print(-1)
		return
	d.sort()
	w = [1] * n
	edges = []
	adj_list = [[] for _ in range(n)]
	for j in range(n - 1, 0, -1):
		(di, i) = d[j]
		pdi = di - n + 2 * w[i]
		p = None
		(lo, hi) = (0, j)
		while lo < hi:
			mid = (lo + hi) // 2
			(xdi, xi) = d[mid]
			if xdi == pdi:
				p = xi
				break
			elif xdi < pdi:
				lo = mid + 1
			else:
				hi = mid
		if p is None:
			print(-1)
			return
		(u, v) = (i, p)
		if v < u:
			(u, v) = (v, u)
		edges.append((u + 1, v + 1))
		adj_list[u].append(v)
		adj_list[v].append(u)
		w[p] += w[i]
	(d0, r) = d[0]
	visited = [False] * n
	x = dfs(r, adj_list, 0, visited)
	if x != d0:
		print(-1)
		return
	edges.sort()
	for uv in edges:
		(u, v) = uv
		print('{} {}'.format(u, v))

def main():
	n = input()
	n = int(n)
	d = []
	for i in range(n):
		di = input()
		di = int(di)
		d.append((di, i))
	solve(n, d)
main()