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>
using namespace std;
typedef int sign;
typedef long long ll;
#define For(i,a,b) for(register sign i=(sign)(a);i<=(sign)(b);++i)
#define Fordown(i,a,b) for(register sign i=(sign)(a);i>=(sign)(b);--i)
const int N=1e5+5;
template<typename T>bool cmax(T &a,T b){return (a<b)?a=b,1:0;}
template<typename T>bool cmin(T &a,T b){return (a>b)?a=b,1:0;}
template<typename T>T read()
{
	T ans=0,f=1;
	char ch=getchar();
	while(!isdigit(ch)&&ch!='-')ch=getchar();
	if(ch=='-')f=-1,ch=getchar();
	while(isdigit(ch))ans=(ans<<3)+(ans<<1)+(ch-'0'),ch=getchar();
	return ans*f;
}
template<typename T>void write(T x,char y)
{
	if(x==0)
	{
		putchar('0'),putchar(y);
		return;
	}
	if(x<0)
	{
		putchar('-');
		x=-x;
	}
	static char wr[20];
	int top=0;
	for(;x;x/=10)wr[++top]=x%10+'0';
	while(top)putchar(wr[top--]);
	putchar(y);
}
void file()
{
#ifndef ONLINE_JUDGE
	freopen("in","r",stdin);
	freopen("out","w",stdout);
#endif
}
char s[N];
int n;
void input()
{
	scanf("%s",s+1);
	n=strlen(s+1);
}
bool check()
{
	if(s[1]=='0'||s[n]=='1'||s[n-1]=='0')return false;
	For(i,1,n-1)if(s[i]!=s[n-i])return false;
	return true;
}
bool used[N];
vector<int>E;
int now;
void work()
{
	now=1;
	if(!check()){puts("-1");return;}	
	For(i,1,n)if(s[i]=='1')used[i]=1,E.push_back(i);
	For(i,1,E.size()-1)
	{
		printf("%d %d\n",E[i-1],E[i]);
		For(j,1,E[i]-E[i-1]-1)
		{
			while(used[now])now++;
			printf("%d %d\n",E[i],now++);
		}
	}
	//cerr<<now<<' '<<n<<endl;
	For(i,now,n)if(!used[i])printf("%d %d",i,n-1);
}
int main()
{
//	file();
	input();
	work();
	return 0;
}