Given a string s containing just the characters '(', ')', '{', '}', '[' and ']', determine if the input string is valid.

An input string is valid if:

1. Open brackets are closed by the same type of brackets.
2. Open brackets are closed in the correct order.
3. Every close bracket has a corresponding open bracket of the same type.

Example: s = "()[]{}" → true. s = "([)]" → false (a square bracket closes a parenthesis).