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

Examples

Example 1

Input:  s = "()"
Output: true

Example 2

Input:  s = "()[]{}"
Output: true

Example 3

Input:  s = "(]"
Output: false

Example 4

Input:  s = "([])"
Output: true

Example 5

Input:  s = "([)]"
Output: false

Constraints

• 1 <= s.length <= 10⁴
• s consists of parentheses only '()[]{}'.