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 Rust (1.15.1) (judge verdict: Accepted)

// https://atcoder.jp/contests/arc103/tasks/arc103_d
//
#![allow(unused_imports)]
use std::io::*;
use std::fmt::*;
use std::str::*;
use std::cmp::*;
use std::collections::*;

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($iter:expr, [ next / $t:tt ]) => {
        {
            let len = read_value!($iter, usize);
            (0..len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
        }
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_macros)]
macro_rules! dvec {
    ($t:expr ; $len:expr) => {
        vec![$t; $len]
    };

    ($t:expr ; $len:expr, $($rest:expr),*) => {
        vec![dvec!($t; $($rest),*); $len]
    };
}

#[allow(unused_macros)]
macro_rules! ifv {
    ($t:expr, $a:expr, $b: expr) => {
        if $t { $a } else { $b }
    }
}

#[allow(unused_macros)]
macro_rules! fill {
    ($t:expr, $v:expr) => {
        for i in 0..$t.len() {
            $t[i] = $v;
        }
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        println!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
    }
}

fn main() {
    input! {
        n: usize,
        d: [i64; n]
    };
    let mut d = d.into_iter().zip(0..n).collect::<Vec<_>>();
    d.sort_by_key(|&(w,idx)| -w);

    let mut dmap = HashMap::new();
    for i in 0..n {
        dmap.insert(d[i].0, d[i].1);
    }

    let n64 = n as i64;
    let mut edges = vec![];
    let mut used = vec![false; n];
    let mut cnt = vec![1; n];

    let mut is_ok = true;
    for &(dist,vidx) in &d {
        let to_dist = dist - n64 + cnt[vidx] * 2;
        if to_dist > dist {
            continue;
        }
        // debug!(dist, to_dist, dmap.get(&to_dist));
        match dmap.get(&to_dist) {
            None => {
                is_ok = false;
                break;
            },
            Some(&idx) => {
                edges.push((vidx,idx));
                cnt[idx] += cnt[vidx];
            }
        }
    }

    is_ok &= edges.len() == n-1;

    d.sort_by_key(|&(w,idx)| idx);
    if is_ok {
        is_ok &= try_make(&d, &edges);
    }

    if is_ok {
        for (u, v) in edges {
            println!("{} {}", u+1, v+1);
        }
    } else {
        println!("-1");
    }


}

fn try_make(d: &Vec<(i64, usize)>, edges: &Vec<(usize, usize)>) -> bool {
    let n = edges.len()+1;
    let mut graph = vec![vec![]; n];
    for &(u,v) in edges {
        graph[u].push(v);
        graph[v].push(u);
    }
    let (nn, d0) = dfs(0, None, &graph);
    d[0].0 == d0
}

fn dfs(now: usize, par: Option<usize>, graph: &Vec<Vec<usize>>) -> (i64, i64) {
    let mut w = 1;
    let mut total_d = 0;
    for &to in &graph[now] {
        if Some(to) == par {
            continue;
        }
        let (wc, t) = dfs(to, Some(now), graph);
        w += wc;
        total_d += t + wc;
    }
    (w, total_d)
}