The freshmen's code now uses three different kinds of brackets, and half of it doesn't balance at all — Rina's editor must now report the minimum number of characters needed to fix it, not just yes/no. Read a string of '(', ')', '[', ']', '{', '}'. If it's already balanced print "VALID". Otherwise print the MINIMUM number of characters you must insert to make it balanced (insertions only, no deletions or substitutions allowed).
Input
One string S of the six bracket characters.
Output
"VALID" or an integer: minimum insertions needed.
Constraints
1 ≤ |S| ≤ 10^5
Sample Input
([)]
Sample Output
2
main.c
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