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://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 より
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, 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")
    };
}

//

fn run() {
    input! {
        n: usize,
        distance_sum: [i64; n],
    }
    let mut d = distance_sum.iter().cloned().enumerate().collect::<Vec<_>>();
    d.sort_by_key(|d| d.1);
    let mut size = vec![1i64; n];
    let mut edge = Vec::with_capacity(n - 1);
    let mut deg = vec![0; n + 1];
    for i in (1..n).rev() {
        let (a, x) = d[i];
        let y = x - n as i64 + 2 * size[a];
        if let Ok(k) = d.binary_search_by(|d| d.1.cmp(&y)) {
            let b = d[k].0;
            size[b] += size[a];
            edge.push((a, b));
            deg[a] += 1;
            deg[b] += 1;
        } else {
            println!("-1");
            return;
        }
        size[a] = 0;
    }
    if !size.iter().any(|s| *s == n as i64) {
        println!("-1");
        return;
    }
    for i in 1..(n + 1) {
        deg[i] += deg[i - 1];
    }
    let mut buf = vec![0; 2 * (n - 1)];
    for &(a, b) in edge.iter() {
        deg[a] -= 1;
        buf[deg[a]] = b;
        deg[b] -= 1;
        buf[deg[b]] = a;
    }
    let neighbor = |v: usize| &buf[deg[v]..deg[v + 1]];
    let mut q = Vec::with_capacity(n);
    let mut parent = vec![0; n];
    let mut dfs = vec![0];
    while let Some(v) = dfs.pop() {
        q.push(v);
        let p = parent[v];
        for &u in neighbor(v).iter() {
            if u != p {
                parent[u] = v;
                dfs.push(u);
            }
        }
    }
    let mut dp1 = vec![0; n];
    size.clear();
    size.resize(n, 1);
    for &v in q.iter().rev() {
        let p = parent[v];
        for &u in neighbor(v).iter() {
            if u != p {
                dp1[v] += dp1[u] + size[u];
                size[v] += size[u];
            }
        }
    }
    let mut dp2 = dp1.clone();
    for &v in q.iter() {
        let p = parent[v];
        for &u in neighbor(v).iter() {
            if u != p {
                dp2[u] = dp2[v] + n as i64 - size[u] * 2;
            }
        }
    }
    if dp2.iter().zip(distance_sum.iter()).all(|p| *p.0 == *p.1) {
        let mut out = String::new();
        for (a, b) in edge {
            out.push_str(&format!("{} {}\n", a + 1, b + 1));
        }
        print!("{}", out);
    } else {
        println!("-1");
    }
}

fn main() {
    run();
}