Append count after each match

Append count after each match

Sample input:
>Sample GJVT7LS03DEUKL
AAACTCCGCAATGCGCGCAAGC
>Sample GJVT7LS03CXJ53
AAACTCCGCAATGCGCGCAAGCGTGACGGGG
>Sample GJVT7LS03DJOYJ
AAACTCC
>Sample GJVT7LS03DMERH
AAACTCCGCAATGCGCGCAAGCGTGACGGGGGGAC
>Sample GJVT7LS03DN2RB
AAACTCCGCAATGCGCGCAAGCGTGACGG
What I want out:
>Sample_1 GJVT7LS03DEUKL
AAACTCCGCAATGCGCGCAAGC
>Sample_2 GJVT7LS03CXJ53
AAACTCCGCAATGCGCGCAAGCGTGACGGGG
>Sample_3 GJVT7LS03DJOYJ
AAACTCC
>Sample_4 GJVT7LS03DMERH
AAACTCCGCAATGCGCGCAAGCGTGACGGGGGGAC
>Sample_5 GJVT7LS03DN2RB
AAACTCCGCAATGCGCGCAAGCGTGACGG
In other words, I want to append count (preceded by "_") for each line
that matches pattern ("Sample" in this case). Any sed/awk/etc. one-liners
for this task?