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>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<algorithm>
#include<map>
#define ll long long
#define inf 0x3f3f3f3f
#define maxn 200010
inline ll read()
{
	ll x=0; char c=getchar(),f=1;
	for(;c<'0'||'9'<c;c=getchar())if(c=='-')f=-1;
	for(;'0'<=c&&c<='9';c=getchar())x=x*10+c-'0';
	return x*f;
}
inline void write(ll x)
{
	static char buf[20];
	int len=0;
	if(x<0)putchar('-'),x=-x;
	for(;x;x/=10)buf[len++]=x%10+'0';
	if(!len)putchar('0');
	else while(len)putchar(buf[--len]);
}
inline void writesp(ll x){write(x); putchar(' ');}
inline void writeln(ll x){write(x); putchar('\n');}
ll d[maxn];
std::map<ll,int>mp;
int id[maxn],fa[maxn],size[maxn];
int anc[maxn];
int n;
bool cmp(int x,int y){return d[x]>d[y];}
int find(int x){return anc[x]==x?x:anc[x]=find(anc[x]);}
int main()
{
	n=read();
	for(int i=1;i<=n;i++)
		d[i]=read(),mp[d[i]]=i;
	for(int i=1;i<=n;i++)
		id[i]=i,size[i]=1;
	std::sort(id+1,id+n+1,cmp);
	for(int i=1;i<n;i++){
		fa[id[i]]=mp[d[id[i]]-(n-2*size[id[i]])];
		// printf("%d %d %d\n",id[i],size[id[i]],fa[id[i]]);
		if(!fa[id[i]]){
			puts("-1"); return 0;
		}
		size[fa[id[i]]]+=size[id[i]];
	}
	for(int i=1;i<=n;i++)
		anc[i]=i;
	for(int i=1;i<=n;i++)
		if(fa[i]){
			if(find(fa[i])==find(i)){
				puts("-1"); return 0;
			}
			anc[find(i)]=find(fa[i]);
		}
	for(int i=1;i<=n;i++)
		if(fa[i])writesp(fa[i]),writeln(i);
	return 0;
}