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: Accepted)

#include<bits/stdc++.h>
typedef long long ll;
typedef long double ld;
using namespace std;
mt19937_64 mrand(chrono::steady_clock::now().time_since_epoch().count());
#define ii for(int i=1;i<=n;++i)
#define ji for(int j=1;j<=n;++j)
#define jj for(int j=1;j<=m;++j)
#define ij for(int i=1;i<=m;++i)
#define sz(x) ((ll)x.size())
#define all(x) x.begin(),x.end()
#define alll(x) x+1,x+1+n
#define asd cout<<"ok"<<endl;
#define endl '\n'

int a[100005];
int main()
{
    string s;
    cin>>s;
    int n=s.size();
    ii a[i]=(s[i-1]=='1');
    if(a[n]) return cout<<-1<<endl,0;
    if(!a[1] || !a[n-1]) return cout<<-1<<endl,0;
    for(int i=2;i<=n-2;++i) if(a[i] && !a[n-i]) return cout<<-1<<endl,0;
    int tp = 0, rt = 0, sz = 0;
    vector<pair<int,int>> ans;
    for(int i=2;i<=n/2;++i)
    {
        if(a[i])
        {
            ++tp;
            int nxt = tp;
            if(sz) ans.push_back({nxt, rt});
            for(int j=1;j<=i-sz-1;++j) ans.push_back({nxt,++tp});
            rt = nxt;
            sz = i;
        }
    }
    int nxt = ++tp;
    if(sz) ans.push_back({nxt, rt});
    for(int j=1;j<=n-sz-1;++j) ans.push_back({nxt,++tp});
    for(auto p:ans) cout<<p.first<<" "<<p.second<<endl;
}