how to insert space between individual digits in a file?

My data looks like:

$ cat input
1212103122
1233321212
0000022221

I want the output to look like:

$ cat output
1 2 1 2 1 0 3 1 2 2
1 2 3 3 3 2 1 2 1 2
0 0 0 0 0 2 2 2 2 1

I tried:

sed -i 's// /g' input > output

but it does not work.

Any suggestions?