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Prelude to Self-describing Sequence
Input
Output
Sample Input
Sample Output

Prelude to Self-describing Sequence

First, start by reading the problem statement for Self-describing Sequence.

For this prelude, create an array, fr, that contains the index of each place in f(n) where f(n) changes values (that is, where the next run of identical values appears).

n     1   2   3   4   5   6   7   8   9  10  11  12 13 14 15 16
f(n)  1   2   2   3   3   4   4   4   5   5   5   6  6  6  6  7
fr[n] 1   2   4   6   9  12  16   ...

This array is a kind of run-length encoding of function f(n).

Input

Input consists of a sequence of integers, one per line. The last entry is a 0, which should not be processed.

Output

For each non-zero input value, n, print the value of fr[n].

Sample Input

3 1269 1160 1663
3 1 1 1
5 226 223 225 224 227 229 228 226 225 227
5 216 210 204 212 220 214 222 208 216 210
5 -1 0 -1 -2 1 0 -1 1 0 -1
5 79950 79936 79942 79962 79954 79972 79960 79968 79924 79932

Sample Output

3 1160 1269 1663
3 1 1 1
10 223 224 225 225 226 226 227 227 228 229
10 204 208 210 210 212 214 216 216 220 222
10 -2 -1 -1 -1 -1 0 0 0 1 1
10 79924 79932 79936 79942 79950 79954 79960 79962 79968 79972