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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;
import java.io.*;
 
public class Main {
    public static void main(String[] args) throws Exception {
        FastScanner sc = new FastScanner(System.in);
        char[] s = sc.next().toCharArray();
        if(s[0] == '0' || s[s.length-1] == '1'){
            System.out.println(-1);
            return;
        }
        ArrayList<Edge> li = new ArrayList<>();
        boolean is1 = true;
        for(int i = 0; i < s.length/2; i++){
            if(s[i] != s[s.length-2-i] || (s[i] == '1' && !is1)){
                System.out.println(-1);
                return;
            }
            if(i != 0){
                if(is1){
                    li.add(new Edge(i, i+1));
                }else{
                    li.add(new Edge(1, i+1));
                }
            }
            if(s[i] != '1'){
                is1 = false;
            }
        }
        for(Edge e : li){
            System.out.println(e.s + " " + e.g);
        }
        for(int i = s.length/2; i < s.length; i++){
            if(is1){
                System.out.println(i+" "+(i+1));
            }else{
                System.out.println(1+" "+(i+1));
            }
        }
    }
}

class Edge{
    int s,g;
    public Edge(int s, int g){
        this.s = s;
        this.g = g;
    }
}

class WeightedUnionFind{
    int[] parent;
    int[] rank;
    long[] weight;
    int[] size;
 
    public WeightedUnionFind(int size) {
		this.parent = new int[size];
		this.rank = new int[size];
        this.weight = new long[size];
		this.size = new int[size];
		
		for (int i = 0; i < size; i++) {
			makeSet(i);
		}
	}
	
	public void makeSet(int i) {
		parent[i] = i;
		rank[i] = 0;
		size[i] = 1;
	}
 
    public boolean union(int x, int y, long w) {
        w += getWeight(x);
        w -= getWeight(y);
        int xRoot = find(x);
        int yRoot = find(y);
        if(xRoot == yRoot){
            return getDistance(xRoot,yRoot) == w;
        } else if (rank[xRoot] > rank[yRoot]) { 
            parent[yRoot] = xRoot;
            size[xRoot] += size[yRoot];
            weight[yRoot] = w;
        } else if(rank[xRoot] < rank[yRoot]) {
            parent[xRoot] = yRoot;
            size[yRoot] += size[xRoot];
            weight[xRoot] = -w;
        } else if (xRoot != yRoot){
            parent[yRoot] = xRoot;
            size[xRoot] += size[yRoot];
            rank[xRoot]++; 
            weight[yRoot] = w;
        }
        return true;
    }
	
	public int find(int i) {
	    int p = parent[i];
	    if (i != parent[i]) {
	        parent[i] = find(parent[i]);
	        weight[i] += weight[p];
	    }
	    return parent[i];
	}
    
    public long getWeight(int i){
        find(i);
        return weight[i];
    }
    
    public long getDistance(int x, int y) {
        return getWeight(y) - getWeight(x);
    }
	
	public boolean same(int x, int y) {
		return find(x) == find(y);
	}
 
	public int size(int x) {
	    return size[find(x)];
	}
}

class FastScanner {
    private BufferedReader reader = null;
    private StringTokenizer tokenizer = null;
    public FastScanner(InputStream in) {
        reader = new BufferedReader(new InputStreamReader(in));
        tokenizer = null;
    }

    public String next() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public String nextLine() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken("\n");
    }

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

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

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

    public int[] nextIntArray(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = nextInt();
        return a;
    }

    public long[] nextLongArray(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = nextLong();
        return a;
    } 
}