#include <iostream>
#include <algorithm>

using namespace std;

int btoi(string s)
{
	int n=0;
	for(int i=0;i<7;i++){
		n<<=1;
		if(s[i]=='1')
			n++;
	}
	return n;
}
string itob(int n)
{
	string s;
	for(int i=0;i<7;i++)
		s+='0'+(n>>i&1);
	reverse(begin(s),end(s));
	return s;
}

int main()
{
	int ss[]={
		btoi("0111111"), // 0
		btoi("0000110"), // 1
		btoi("1011011"), // 2
		btoi("1001111"), // 3
		btoi("1100110"), // 4
		btoi("1101101"), // 5
		btoi("1111101"), // 6
		btoi("0100111"), // 7
		btoi("1111111"), // 8
		btoi("1101111"), // 9
	};
	
	for(int n;cin>>n,~n;){
		int c=0;
		while(n--){
			int x; cin>>x;
			to_string(x);
			cout<<itob(c^ss[x])<<endl;
			c=ss[x];
		}
	}
	
	return 0;
}
### Prompt

Please create a solution in CPP to the following problem:

The screen that displays digital numbers that you often see on calculators is called a "7-segment display" because the digital numbers consist of seven parts (segments).

The new product to be launched by Wakamatsu will incorporate a 7-segment display into the product, and as an employee, you will create a program to display the given number on the 7-segment display.

This 7-segment display will not change until the next switch instruction is sent. By sending a signal consisting of 7 bits, the display information of each corresponding segment can be switched. Bits have a value of 1 or 0, where 1 stands for "switch" and 0 stands for "as is".

The correspondence between each bit and segment is shown in the figure below. The signal sends 7 bits in the order of "gfedcba". For example, in order to display "0" from the hidden state, "0111111" must be sent to the display as a signal. To change from "0" to "5", send "1010010". If you want to change "5" to "1" in succession, send "1101011".

<image>



Create a program that takes n (1 ≤ n ≤ 100) numbers that you want to display and outputs the signal sequence required to correctly display those numbers di (0 ≤ di ≤ 9) on the 7-segment display. please. It is assumed that the initial state of the 7-segment display is all hidden.



Input

A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of -1. Each dataset is given in the following format:


n
d1
d2
::
dn


The number of datasets does not exceed 120.

Output

For each input dataset, output the sequence of signals needed to properly output the numbers to the display.

Example

Input

3
0
5
1
1
0
-1


Output

0111111
1010010
1101011
0111111

### Response

```cpp
#include <iostream>
#include <algorithm>

using namespace std;

int btoi(string s)
{
	int n=0;
	for(int i=0;i<7;i++){
		n<<=1;
		if(s[i]=='1')
			n++;
	}
	return n;
}
string itob(int n)
{
	string s;
	for(int i=0;i<7;i++)
		s+='0'+(n>>i&1);
	reverse(begin(s),end(s));
	return s;
}

int main()
{
	int ss[]={
		btoi("0111111"), // 0
		btoi("0000110"), // 1
		btoi("1011011"), // 2
		btoi("1001111"), // 3
		btoi("1100110"), // 4
		btoi("1101101"), // 5
		btoi("1111101"), // 6
		btoi("0100111"), // 7
		btoi("1111111"), // 8
		btoi("1101111"), // 9
	};
	
	for(int n;cin>>n,~n;){
		int c=0;
		while(n--){
			int x; cin>>x;
			to_string(x);
			cout<<itob(c^ss[x])<<endl;
			c=ss[x];
		}
	}
	
	return 0;
}
```