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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>

#define int long long
#define double long double
#define ff first
#define ss second
#define endl '\n'
#define ii pair<int, int>
#define DESYNC ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0)
#define pb push_back
#define vi vector<int>
#define vii vector< ii >
#define EPS 1e-9
#define INF 1e18
#define ROOT 1
#define M 1000000007
const double PI = acos(-1);

using namespace std;

inline int mod(int n, int m){ int ret = n%m; if(ret < 0) ret += m; return ret; }

int gcd(int a, int b){
  if(a == 0 || b == 0) return 0;
  else return abs(__gcd(a,b));
}

string s;
int n;

int32_t main(){
  DESYNC;
  cin >>s;
  n = s.size();
  if(s[n-1] == '1'){
    cout << -1 << endl;
    return 0;
  }
  if(s[0] == '1' && s[n-2] == '1'){
    for(int i=1; i<n; i++) cout << i << " " << n << endl;
    return 0;
  }
  cout << -1 << endl;
}