/*
 * this class solve the problem of "Hide that Number"
 * Briefly: given a number 123, crypt it as follows:
 * 123 * 10 + 123 = 1353, cut the any extra leading digit
 * so 123 --> 353
 * This program has the:
 * hide method: to hide/encrypt number
 * unhid method: to unhide the number if possoble.
 */

public class HideThatNumber {
	public static void main(String[] agrs){
		for(int i=1;i<10000;i++){
			String hidden = i+"";		
			String t2 = unhide( hidden );
			
			System.out.println( hidden  + " -->" + t2 + "==>" + 
			( (hidden.length()!= t2.length()) ? "Imposible":""));
		}
		
		String num = "1234567890123456789001234567890";
		System.out.println("hiding: " + num);
		System.out.println(hide(num)+ "-->" + unhide(hide(num)));
		num = "123456";
		System.out.println(unhide(num));

	}	

	
	// hide method that does not consider large integers.
	public static int hide(int n){
		int m = n * 10;
		m = m + n;
		int ll = len(m) - len(n);
		if( ll == 0) return m;
		else{
			return Integer.parseInt( (m +"").substring(1));
		}
			
	}
	/* this method hides numbers in the format of string
	 * That is because integer format is limited and cannot hold
	 * big number of too many digits.
	 */
	public static String hide(String num){
		StringBuffer sb = new StringBuffer(num);
		StringBuffer orig = new StringBuffer(num);
		orig.insert(0,'0');
		StringBuffer result = new StringBuffer();
		sb.append('0');
		int c = 0;
		for(int i=orig.length()-1;i>=0;i--){
			int d1 = sb.charAt(i) - '0';
			int d2 = orig.charAt(i) - '0';
			int res = d1 + d2 + c;
			//System.out.println(d1 + "+" + d2 + "+ "+ c +" =" + res);
			if(res >9){			
				int digit = res % 10;
				c = res / 10;
				result.insert(0,digit);
			}else{
				result.insert(0,res);
				c=0;
			}
		}
		if(c != 0) result.insert(0,c);
		//cut extra digits more than the original
		int l = result.length() - orig.length() + 1;
		result = new StringBuffer(result.substring(l));

		//remove any leading zeros...
		for(int i=0;i<result.length();i++)
			if(result.charAt(i) == '0') result.setCharAt(i,' ');
			else break;
		return result.toString().trim();
		
	}
	
	
	// works but for small integers (does not handle overflows
	public static void unhide(int n){
		boolean flag = false;
		for(int i = 1; i <= 20 ;i++){ 
			int x = putLeft( n, i);
			if( ( x % 11 == 0) ){					
				int orig = x /11;
				if( len(orig) == len(n)){
					System.out.println( "unhiding:" + n + "-->"  + (x/11) );
					flag = true;
				}
			}
		}
		if(!flag) System.out.println(n +"--> Impossible");		
	}
	
	public static int len(int n){
		int m = 0;
		while( n > 0) {
			m++;
			n/=10;
		}
		return m;
	}
		
	public static int putLeft(int n, int rm){
		String s = n +"";
		int v = 1;
		for(int i=0;i<s.length();i++){
			v = v * 10;
		}
		return n + rm * v;
	}
	
	/*
	 * this method unhide the number in the format of string
	 * 
	 */
	public static String unhide(String num){
		StringBuffer sb = new StringBuffer();
		int curHidden = num.charAt(num.length()- 1) - '0';
		sb.insert(0,curHidden);
		int borrow = 0;
		for(int i= num.length()-2;i>=0;i--){			
			int dif = (num.charAt(i) - '0') - curHidden;			
			if(borrow == 1) dif--;			
			if(dif < 0) {
				sb.insert(0, dif+10);
				borrow = 1;
				curHidden = dif+10;
			}else if( dif >= 0){
					sb.insert(0,dif);
					curHidden = dif;
					if(borrow == 1) borrow = 0;
			}			
		}
		//remove zeros...
		for(int i=0;i<sb.length();i++){
			if(sb.charAt(i) == '0') sb.setCharAt(i, ' ');
			else break;
		}
		return sb.toString().trim();
	}
}