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)

#pragma GCC optimize ("O3")
#include <bits/stdc++.h>
#define endl "\n"
#define sz(x) ((ll)(x).size())
#define pb push_back
#define all(x) (x).begin(),(x).end()
#define prt(x) cout << (x)
#define prtl(x) cout << (x) << endl
#define rep(i,a,b) for(ll i=a; i<b; i++)
#define rrep(i,a,b) for(ll i=a; i>b; i--)
#define mp(a, b) make_pair(a, b)
#define chmin(x, y) x = min(x, y)
#define chmax(x, y) x = max(x, y)
using namespace std;
using vi = vector<int>;
using vll = vector<long long int>;
using vb = vector<bool>;
using vvb = vector<vector<bool>>;
using vc = vector<char>;
using vvi = vector<vector<int>>;
using vvll = vector<vector<long long int>>;
using vvc = vector<vector<char>>;
using ll = long long int;
using P = pair<long long int, long long int>;
using Map = map<long long int, long long int>;
ll INF = 1LL<<60;
ll M = 1000000007;

int main(){
    string s; cin >> s;
    ll n = sz(s);
    if(s[0]=='0'||s[n-1]=='1'){
        prt(-1);
    }else{

    }
}