Problem:
Score : 900 points

Problem Statement

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 1

7
10
15
13
18
11
14
19

Sample Output 1

1 2
1 3
1 5
3 4
5 6
6 7

The tree shown below satisfies the conditions.

Sample Input 2

2
1
2

Sample Output 2

-1

Sample Input 3

15
57
62
47
45
42
74
90
75
54
50
66
63
77
87
51

Sample Output 3

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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<cstdio>

int n,nn;
struct node{int p,f,l,r;long long d;};
node a[100010];
int oa[100010],ob[100010];

void qsort(int l,int r)
{
	int i,j;
	node m,t;
	i=l;j=r;
	m=a[(l+r)/2];
	while (i<=j)
	{
		while (a[i].d<m.d) i++;
		while (a[j].d>m.d) j--;
		if (i<=j)
		{
			t=a[i];a[i]=a[j];a[j]=t;
			i++;j--;
		}
	}
	if (l<j) qsort(l,j);
	if (i<r) qsort(i,r);
}

void qsort2(int l,int r)
{
	int i,j;
	int ma,mb,t;
	i=l;j=r;
	ma=oa[(l+r)/2];
	mb=ob[(l+r)/2];
	while (i<=j)
	{
		while (oa[i]<ma || (oa[i]==ma && ob[i]<mb)) i++;
		while (oa[j]>ma || (oa[j]==ma && ob[j]>mb)) j--;
		if (i<=j)
		{
			t=oa[i];oa[i]=oa[j];oa[j]=t;
			t=ob[i];ob[i]=ob[j];ob[j]=t;
			i++;j--;
		}
	}
	if (l<j) qsort2(l,j);
	if (i<r) qsort2(i,r);
}

int main()
{
	scanf("%d",&n);
	nn=n-2;
	for (int i=1;i<=n;i++)
	{
		scanf("%lld",&a[i].d);
		a[i].p=i;
		a[i].f=-1;
		a[i].l=-1;
		a[i].r=-1;
	}
	qsort(1,n);
	bool ok=true;
	a[1].l=0;a[1].r=n-1;
	for (int i=2;i<=n;i++)
	{
		bool check=true;
		for (int j=i-1;j>=1;j--)
		{
			if (a[i].d-a[j].d>nn) 
			{
				check=false;break;
			}
			else
			{
				if ((a[i].d-a[j].d-nn)%2==0)
				{
					int l,r;
					l=(nn+(a[i].d-a[j].d))/2;
					r=(nn-(a[i].d-a[j].d))/2;
					if (r<a[j].r)
					{
						a[i].f=a[j].p;
						a[i].l=nn-r;
						a[i].r=r;
						break;
					}
				}
			}
		}
		if (!check) {ok=false;break;}
	}
	if (ok)
	{
		for (int i=1;i<=n;i++)
		{
			if (a[i].f<a[i].p) {oa[i]=a[i].f;ob[i]=a[i].p;}
			else {oa[i]=a[i].p;ob[i]=a[i].f;}
		}
		qsort2(1,n);
		for (int i=2;i<=n;i++)
			printf("%d %d\n",oa[i],ob[i]);
	}
	else printf("-1");
}