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<bits/stdc++.h>
#define	INF	0x3f3f3f3f
#define	LL	long long
#define	MAXN	100010
using namespace std;
LL minn;
int n, size[MAXN], fa[MAXN], F[MAXN];
struct info{LL w; int id;}a[MAXN];

bool operator < (info a, info b){
	return a.w < b.w;
}

template <typename T> void chkmin(T &x, T y){x = min(x, y);}
template <typename T> void chkmax(T &x, T y){x = max(x, y);}
template <typename T> void read(T &x){
	x = 0; int f = 1; char ch = getchar();
	while (!isdigit(ch)) {if (ch == '-') f = -1; ch = getchar();}
	while (isdigit(ch)) {x = x * 10 + ch - '0'; ch = getchar();}
	x *= f;
}

int find(int x){
	if (fa[x] == x) return fa[x];
	else return (fa[x] = find(fa[x]));
}

int merge(int x, int y){
	int fx = find(x), fy = find(y);
	if (fx == fy) return 0;
	fa[fx] = fy;
	return 1;
}

int main(){
	read(n);
	minn = 1ll * INF * INF;
	for (int i = 1; i <= n; ++i){
		read(a[i].w), a[i].id = i;
		chkmin(minn, a[i].w);
	}
	for (int i = 1; i <= n; ++i)
		size[i] = 1, fa[i] = i;
	sort(a + 1, a + 1 + n);
	for (int i = n; i > 1; --i){
		int cur = a[i].id;
		LL vf = a[i].w + 2 * size[cur] - n;
		//printf("%d %lld\n", cur, vf);
		int f = lower_bound(a + 1, a + 1 + n, (info){vf, 0}) - a;
		if (a[f].w != vf) {printf("-1\n"); return 0;}
		f = a[f].id;
		//printf("%d\n", f);
		int fla = merge(cur, f);
		if (!fla) {printf("-1\n"); return 0;}
		F[cur] = f;
		size[f] += size[cur];
	}
	for (int i = 1; i <= n; ++i){
		if (a[i].w == minn) continue;
		printf("%d %d\n", a[i].id, F[a[i].id]);
	}
	return 0;
}