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 Pascal (FPC 2.6.2) (judge verdict: Wrong Answer)

var
  n,i,j,k,t,root:longint;
  a:array[1..10000] of integer;
  x:char;
  first,next,last,b:array[1..100000] of longint;
begin
  i:=0;
  while not eoln do
    begin
      n:=n+1;
      read(x);
      if x='1'
        then a[n]:=1
        else a[n]:=0;
    end;
  if (a[1]=0)or(a[n]=1)
    then
      begin
        writeln(-1);
        halt;
      end;
  for i:=2 to n div 2 do
    if (a[i]=1)and(a[n-i]=0)
      then
        begin
          writeln(-1);
          halt;
        end;
  root:=1;
  writeln(1,' ',2);
  if a[2]=1
    then root:=2;
  for i:=3 to n do
    if a[i-1]=0
      then writeln(root,' ',i)
      else
        begin
          writeln(root,' ',i);
          root:=i;
        end;
end.