Problem: Polycarp studies at the university in the group which consists of n students (including himself). All they are registrated in the social net "TheContacnt!".

Not all students are equally sociable. About each student you know the value ai — the maximum number of messages which the i-th student is agree to send per day. The student can't send messages to himself. 

In early morning Polycarp knew important news that the programming credit will be tomorrow. For this reason it is necessary to urgently inform all groupmates about this news using private messages. 

Your task is to make a plan of using private messages, so that:

  * the student i sends no more than ai messages (for all i from 1 to n); 
  * all students knew the news about the credit (initially only Polycarp knew it); 
  * the student can inform the other student only if he knows it himself. 



Let's consider that all students are numerated by distinct numbers from 1 to n, and Polycarp always has the number 1.

In that task you shouldn't minimize the number of messages, the moment of time, when all knew about credit or some other parameters. Find any way how to use private messages which satisfies requirements above. 

Input

The first line contains the positive integer n (2 ≤ n ≤ 100) — the number of students. 

The second line contains the sequence a1, a2, ..., an (0 ≤ ai ≤ 100), where ai equals to the maximum number of messages which can the i-th student agree to send. Consider that Polycarp always has the number 1.

Output

Print -1 to the first line if it is impossible to inform all students about credit. 

Otherwise, in the first line print the integer k — the number of messages which will be sent. In each of the next k lines print two distinct integers f and t, meaning that the student number f sent the message with news to the student number t. All messages should be printed in chronological order. It means that the student, who is sending the message, must already know this news. It is assumed that students can receive repeated messages with news of the credit. 

If there are several answers, it is acceptable to print any of them. 

Examples

Input

4
1 2 1 0


Output

3
1 2
2 4
2 3


Input

6
2 0 1 3 2 0


Output

6
1 3
3 4
1 2
4 5
5 6
4 6


Input

3
0 2 2


Output

-1

Note

In the first test Polycarp (the student number 1) can send the message to the student number 2, who after that can send the message to students number 3 and 4. Thus, all students knew about the credit. 

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Iterator;
import java.io.BufferedWriter;
import java.util.Collection;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Jialin Ouyang (Jialin.Ouyang@gmail.com)
 */
public class Main {
  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    QuickScanner in = new QuickScanner(inputStream);
    QuickWriter out = new QuickWriter(outputStream);
    TaskB solver = new TaskB();
    solver.solve(1, in, out);
    out.close();
  }

  static class TaskB {
    int n;
    Student[] students;
    IntArrayList resX;
    IntArrayList resY;

    public void solve(int testNumber, QuickScanner in, QuickWriter out) {
      n = in.nextInt();
      students = new Student[n];
      for (int i = 0; i < n; ++i) {
        students[i] = new Student(in.nextInt(), i);
      }
      Arrays.sort(students, 1, n);
      resX = new IntArrayList(n);
      resY = new IntArrayList(n);
      int j = 1;
      for (int i = 0; i < j; ++i) {
        for (int k = 0; j < n && k < students[i].cnt; ++j, ++k) {
          resX.add(students[i].idx);
          resY.add(students[j].idx);
        }
      }
      if (j == n) {
        out.println(n - 1);
        for (int i = 0; i < n - 1; ++i) {
          out.print(resX.get(i) + 1);
          out.print(' ');
          out.println(resY.get(i) + 1);
        }
      } else {
        out.println(-1);
      }
    }

    class Student implements Comparable<Student> {
      final int cnt;
      final int idx;

      public Student(int cnt, int idx) {
        this.cnt = cnt;
        this.idx = idx;
      }


      public int compareTo(Student o) {
        return o.cnt - cnt;
      }

    }

  }

  static class IntUtils {
    public static boolean isPow2(int n) {
      return n > 0 && (n & (n - 1)) == 0;
    }

    public static int nextPow2(int n) {
      if (n < 1) return 1;
      return isPow2(n) ? n : Integer.highestOneBit(n) << 1;
    }

  }

  static class QuickScanner {
    private static final int BUFFER_SIZE = 1024;
    private InputStream stream;
    private byte[] buffer;
    private int currentPosition;
    private int numberOfChars;

    public QuickScanner(InputStream stream) {
      this.stream = stream;
      this.buffer = new byte[BUFFER_SIZE];
      this.currentPosition = 0;
      this.numberOfChars = 0;
    }

    public int nextInt() {
      int c = nextNonSpaceChar();
      boolean positive = true;
      if (c == '-') {
        positive = false;
        c = nextChar();
      }
      int res = 0;
      do {
        if (c < '0' || '9' < c) throw new RuntimeException();
        res = res * 10 + c - '0';
        c = nextChar();
      } while (!isSpaceChar(c));
      return positive ? res : -res;
    }

    public int nextNonSpaceChar() {
      int res = nextChar();
      for (; isSpaceChar(res) || res < 0; res = nextChar()) ;
      return res;
    }

    public int nextChar() {
      if (numberOfChars == -1) {
        throw new RuntimeException();
      }
      if (currentPosition >= numberOfChars) {
        currentPosition = 0;
        try {
          numberOfChars = stream.read(buffer);
        } catch (Exception e) {
          throw new RuntimeException(e);
        }
        if (numberOfChars <= 0) {
          return -1;
        }
      }
      return buffer[currentPosition++];
    }

    public boolean isSpaceChar(int c) {
      return c == ' ' || c == '\t' || isEndOfLineChar(c);
    }

    public boolean isEndOfLineChar(int c) {
      return c == '\n' || c == '\r' || c < 0;
    }

  }

  static class QuickWriter {
    private final PrintWriter writer;

    public QuickWriter(OutputStream outputStream) {
      this.writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public QuickWriter(Writer writer) {
      this.writer = new PrintWriter(writer);
    }

    public void print(Object... objects) {
      for (int i = 0; i < objects.length; ++i) {
        if (i > 0) {
          writer.print(' ');
        }
        writer.print(objects[i]);
      }
    }

    public void println(Object... objects) {
      print(objects);
      writer.print('\n');
    }

    public void close() {
      writer.close();
    }

  }

  static interface IntCollection {
  }

  static class IntArrayList implements IntCollection, Iterable<Integer> {
    private static final int[] EMPTY = {};
    public int[] values;
    public int size;

    public IntArrayList() {
      values = EMPTY;
      clear();
    }

    public IntArrayList(int capacity) {
      values = new int[IntUtils.nextPow2(capacity)];
      clear();
    }

    public IntArrayList(Collection<Integer> collection) {
      this(collection.size());
      addAll(collection);
    }


    public void clear() {
      size = 0;
    }


    public void add(int value) {
      ensureCapacity(size + 1);
      addInternal(value);
    }


    public void addAll(Collection<Integer> values) {
      ensureCapacity(size + values.size());
      for (int value : values) {
        addInternal(value);
      }
    }

    public int get(int idx) {
      if (idx >= size) throw new ArrayIndexOutOfBoundsException();
      return values[idx];
    }

    public void ensureCapacity(int capacity) {
      if (capacity <= values.length) return;
      int[] newValues = new int[IntUtils.nextPow2(capacity)];
      for (int i = 0; i < size; ++i) {
        newValues[i] = values[i];
      }
      values = newValues;
    }


    public String toString() {
      return IntArrayUtils.toString(values, 0, size);
    }


    public Iterator<Integer> iterator() {
      return new Iterator<Integer>() {
        private int i = 0;


        public boolean hasNext() {
          return i < size;
        }


        public Integer next() {
          return values[i++];
        }
      };
    }

    private void addInternal(int value) {
      values[size++] = value;
    }

  }

  static class IntArrayUtils {
    public static String toString(int[] values, int fromIdx, int toIdx) {
      StringBuilder sb = new StringBuilder("[");
      for (int i = fromIdx; i < toIdx; ++i) {
        if (i != fromIdx) sb.append(", ");
        sb.append(values[i]);
      }
      return sb.append("]").toString();
    }

  }
}