Problem: Oleg writes down the history of the days he lived. For each day he decides if it was good or bad. Oleg calls a non-empty sequence of days a zebra, if it starts with a bad day, ends with a bad day, and good and bad days are alternating in it. Let us denote bad days as 0 and good days as 1. Then, for example, sequences of days 0, 010, 01010 are zebras, while sequences 1, 0110, 0101 are not.

Oleg tells you the story of days he lived in chronological order in form of string consisting of 0 and 1. Now you are interested if it is possible to divide Oleg's life history into several subsequences, each of which is a zebra, and the way it can be done. Each day must belong to exactly one of the subsequences. For each of the subsequences, days forming it must be ordered chronologically. Note that subsequence does not have to be a group of consecutive days. 

Input

In the only line of input data there is a non-empty string s consisting of characters 0 and 1, which describes the history of Oleg's life. Its length (denoted as |s|) does not exceed 200 000 characters.

Output

If there is a way to divide history into zebra subsequences, in the first line of output you should print an integer k (1 ≤ k ≤ |s|), the resulting number of subsequences. In the i-th of following k lines first print the integer li (1 ≤ li ≤ |s|), which is the length of the i-th subsequence, and then li indices of days forming the subsequence. Indices must follow in ascending order. Days are numbered starting from 1. Each index from 1 to n must belong to exactly one subsequence. If there is no way to divide day history into zebra subsequences, print -1.

Subsequences may be printed in any order. If there are several solutions, you may print any of them. You do not have to minimize nor maximize the value of k.

Examples

Input

0010100


Output

3
3 1 3 4
3 2 5 6
1 7


Input

111


Output

-1

Solution (in JAVA):

Solution:
import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.LinkedList;
import java.util.List;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.SortedSet;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class Code {
    public static void main(String[] args) {
        // Use the Scanner class
        MyScanner sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));

        String L = sc.nextLine();

        List<Sequence> ans = new ArrayList<>();
        SortedSet<Sequence> zeros_bst = new TreeSet<>();
        SortedSet<Sequence> ones_bst = new TreeSet<>();
        boolean turn = false; // we start with zeros

        for (int i = 0; i < L.length(); ++i) {
            turn = L.charAt(i) == '0' ? false : true;
            SortedSet<Sequence> cur_set = !turn ? ones_bst : zeros_bst; // if turn is false, we look for a sequence that ends with one
            SortedSet<Sequence> other_set = !turn ? zeros_bst : ones_bst; // if turn is true, we look for a sequence that ends with zeros

            int idx = i + 1;
            Sequence s = find_sequence(cur_set, idx, turn);
            // If we can't find a sequence that ends with zero, break
            if (s == null && turn == true) {
                System.out.println("-1");
                return;
            } else if (s == null && turn == false) {
                s = new Sequence();
                ans.add(s);
            }
            cur_set.remove(s);
            s.idx.add(idx);
            s.last_idx = idx;
            other_set.add(s);
        }

        if (!ones_bst.isEmpty()) {
            System.out.println("-1");
            return;

        }

        StringBuilder sb = new StringBuilder();
        sb.append(ans.size());
        for (Sequence seq : ans) {
            sb.append("\n");
            sb.append(seq.idx.size());
            for (int x : seq.idx) {
                sb.append(" " + x);
            }
        }
        System.out.println(sb.toString());
    }

    static Sequence find_sequence(SortedSet<Sequence> bst, int idx, boolean type) {
        Sequence target = new Sequence();
        target.last_idx = idx;
        SortedSet<Sequence> hs = bst.headSet(target);
        Sequence ans = hs.isEmpty() ? null : hs.last();
        //System.out.println(String.format("For idx %d found sequence %s", idx, ans));
        return ans;
    }

    static class Sequence implements Comparable<Sequence> {
        List<Integer> idx;
        int last_idx;

        public Sequence() {
            idx = new ArrayList<>();
            last_idx = 0;
        }

        @Override
        public int compareTo(Sequence o) {
            return Integer.compare(this.last_idx, o.last_idx);
        }

        @Override
        public String toString() {
            String res = idx.size() + " " + idx.toString();
            return res;
        }
    }




    static class Event implements Comparable<Event> {
        int time;
        int type; // start is zero, end is 1

        public Event(int time, int type) {
            this.time = time;
            this.type = type;
        }

        @Override
        public int compareTo(Event o) {
            if (o.time != this.time) {
                return Integer.compare(this.time, o.time);
            }
            return Integer.compare(type, o.type);
        }

    }

    static int minimize_schedule(Day[] days, int n, int m, int k) {
        PriorityQueue<Day> q = new PriorityQueue<Day>(Collections.reverseOrder());
        for (int i = 0; i < n ; ++i) {
            q.add(days[i]);
        }

        int total_hours = Arrays.stream(days).mapToInt(d-> new Integer(d.initial_hours)).sum();
        int hours_saved = 0;
        while (k-- > 0) {
            Day cur = q.poll();
            hours_saved += cur.hours_saved;
            cur.update_day();
            q.add(cur);
        }

        return total_hours - hours_saved;
    }

    static class Day implements Comparable<Day> {
        int day_idx;
        String schedule;
        int hours_saved;
        int initial_hours;

        int start_idx;
        int end_idx;

        public Day(int day_idx, String schedule) {
            this.day_idx = day_idx;
            this.schedule = schedule;

            this.hours_saved = 0;

            this.init_day();
        }

        public void init_day() {
            start_idx = schedule.indexOf('1');
            end_idx = schedule.lastIndexOf('1');

            if (start_idx == -1) {
                initial_hours = 0;
            } else {
                initial_hours = end_idx - start_idx + 1;
            }
            hours_saved = max_saveable_hours();

        }

        public int max_saveable_hours() {
            if (end_idx < start_idx) {
                return 0;
            }
            if (end_idx == start_idx) {
                return 1;
            }
            int s_next = schedule.indexOf('1', 1 + start_idx);
            int e_next = schedule.lastIndexOf('1', end_idx - 1 );
            return Math.max(s_next -start_idx, end_idx - e_next);
        }

        public void update_day() {
            if (start_idx > end_idx) {
                return;
            }

            if (start_idx == end_idx) {
                start_idx++;
                end_idx--;

                hours_saved = max_saveable_hours();
                return;
            }

            int s_next = schedule.indexOf('1', 1 + start_idx);
            int e_next = schedule.lastIndexOf('1', end_idx - 1 );

            if (s_next - start_idx > end_idx - e_next) {
                start_idx = s_next;
            } else {
                end_idx = e_next;
            }
            hours_saved = max_saveable_hours();
        }

        @Override
        public int compareTo(Day o) {
            return Integer.compare(this.hours_saved, o.hours_saved);
        }
    }


    public static PrintWriter out;

    //-----------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;
       }

    }
}