Description

Farmer John has been branding the cows with a serial number ever since he started the farm. The new cow fad is 'RADAR' brands, so-called because they read the same forwards and backwards (they are palindromic). All the cows want their daughters branded in the new RADAR style.

Each mother wants her daughter's brand to be derived from her own non-RADAR brand by summing the mother's brand and its reverse. Sometimes (e.g., 12 + 21 = 33) this yields a RADAR palindrome right away. Sometimes the process must be repeated several times until a RADAR brand emerges. Consider the brand '87' that requires four steps to convert to a RADAR brand:

```          Brand  Reverse   Sum
Step 1:   87 +    78 =  165
Step 2:  165 +   561 =  726
Step 3:  726 +   627 = 1353
Step 4: 1353 +  3531 = 4884```

Given the mother's brand (a positive integer), determine the number of steps and ultimate RADAR brand that results from applying the procedure above. No answer will be greater than two billion.

Input

The input file contains multiple test cases, for each test case:

* Line 1: A single integer, the mother's non-RADAR brand.

Process till EOF.

Output

For each test case, output:

* Line 1: Two space-separated integers, respectively: the number of steps to find the RADAR brand and the ultimate RADAR brand.

```87
```

Sample Output

```4 4884
```

USACO 2006 March