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 rep(i, a, n) for(int i = a; i < n; i++)
#define repr(i, a, b) for(int i = a; i >= b; i--)
#define int long long
#define all(a) a.begin(), a.end()
#define chmax(x, y) x = max(x, y)
#define chmin(x, y) x = min(x, y)
using namespace std;
typedef pair<int, int> P;
const int mod = 1000000007;
const int INF = 1e15;

signed main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    string s;
    cin >> s;
    int n = s.size();
    bool ans = true;
    if(s[0] == '0') ans = false;
    if(s[n - 1] == '1') ans = false;
    int MAX = 0;
    rep(i, 0, n / 2){
        if(s[i] != s[n - 2 - i]) ans = false;
        if(s[i] == '1') MAX = i;
    }
    rep(i, 0, MAX){
        if(s[i] == '0') ans = false;
    }
    if(!ans){
        cout << -1 << endl;
        return 0;
    }
    MAX++;
    int i = 1;
    vector<P> g;
    while(i < n){
        int now = 0;
        rep(j, 0, MAX){
            g.push_back({now, i});
            now = i;
            i++;
            if(i == n) break;
        }
    }
    for(int ii = 0; ii < g.size(); ii++){
        cout << g[ii].first + 1 << ' ' << g[ii].second + 1 << endl;
    }
}