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:
n = int(input())
a = []
s = []

for i in range(n):
    x = int(input())
    a.append(x * n + i)
    s.append(1)

a.sort()
a.reverse()
a.append(-1)
Sum = 0

Have = True

result = []

for i in range(n - 1):
    l = 0
    r = n

    val = (a[i] // n) + s[i] + s[i] - n

    while (l < r):
        m = (l + r + 2) // 2

        if (a[m] >= val * n):
            l = m
        else:
            r = m - 1

    if((a[l] // n) != val):
        Have = False
        break

    s[l] += s[i]
    Sum  += s[i]
    result.append([a[i] % n,a[l] % n])

if (Sum != (a[n - 1] // n)):
    Have = False

if (Have == False):
    print("-1")
else:
    for e in result:
        print(e[0] + 1,end = " ")
        print(e[1] + 1)