Problem:
Score : 700 points

Problem Statement

You are given a string s of length n.
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.

If the i-th character in s is 1, we can have a connected component of size i by removing one edge from the tree.

If the i-th character in s is 0, we cannot have a connected component of size i by removing any one edge from the tree.

If such a tree exists, construct one such tree.

Constraints

2 \leq n \leq 10^5

s is a string of length n consisting of 0 and 1.

Input

Input is given from Standard Input in the following format:

s

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

1111

Sample Output 1

-1

It is impossible to have a connected component of size n after removing one edge from a tree with n vertices.

Sample Input 2

1110

Sample Output 2

1 2
2 3
3 4

If Edge 1 or Edge 3 is removed, we will have a connected component of size 1 and another of size 3. If Edge 2 is removed, we will have two connected components, each of size 2.

Sample Input 3

1010

Sample Output 3

1 2
1 3
1 4

Removing any edge will result in a connected component of size 1 and another of size 3.

Solution in Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.*;
import java.io.*;

public class Main {
    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
        String s = sc.next();
        int n = s.length();
        int [] c = new int[n + 1];
        for (int i = 1; i <= n; i++) c[i] = s.charAt(i - 1) - '0';
        if (c[n] == 1 || c[1] == 0 || c[n - 1] == 0) {
            out.println(-1);
            out.close();
            return;
        }
        boolean ok = true;
        for (int i = 1; i <= n - 1; i++) if (c[i] != c[n - i]) ok = false;
        if (!ok) {
            out.println(-1);
            out.close();
        }
        ArrayList<Integer> a = new ArrayList<>();
        for (int i = 1; i < n; i++) if (c[i] == 1) a.add(i);
        ArrayList<Edge> res = new ArrayList<>();
        int root = 1; int sz = n; int cur = 2;
        Collections.sort(a, Comparator.reverseOrder());
        int idx = 0;
        while (idx < a.size()) {
            for (int i = 0; i < sz - a.get(idx) - 1; i++) {
                res.add(new Edge(root, cur++));
            }
            int nextRoot = cur;
            res.add(new Edge(root, cur++));
            root = nextRoot; sz = a.get(idx);
            ++idx;
        }
        for (Edge e: res) out.println(e.a + " " + e.b);
        out.close();
    }

    static class Edge {
        int a; int b;
        Edge(int a, int b) {
            this.a = a; this.b = b;
        }
    }


    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }


    }

}