You are given a string s consisting of digits. Perform the following operation repeatedly until the string has exactly two digits:

• For each pair of consecutive digits in s, starting from the first digit, calculate a new digit as the sum of the two digits modulo 10.
• Replace s with the sequence of newly calculated digits, maintaining the order in which they are computed.

Return true if the final two digits in s are the same; otherwise, return false.

Examples

Example 1

Input:  s = "3902"
Output: true

Initially, s = "3902" First operation: (s[0] + s[1]) % 10 = (3 + 9) % 10 = 2 (s[1] + s[2]) % 10 = (9 + 0) % 10 = 9 (s[2] + s[3]) % 10 = (0 + 2) % 10 = 2 s becomes "292" Second operation: (s[0] + s[1]) % 10 = (2 + 9) % 10 = 1 (s[1] + s[2]) % 10 = (9 + 2) % 10 = 1 s becomes "11" Since the digits in "11" are the same, the output is true.

Example 2

Input:  s = "34789"
Output: false

Initially, s = "34789". After the first operation, s = "7157". After the second operation, s = "862". After the third operation, s = "48". Since '4' != '8', the output is false.

Constraints

• 3 <= s.length <= 10⁵
• s consists of only digits.