Iris has just learned about IPv4 subnets.

Given a subnet and several IP addresses, please help Iris determine whether each address belongs to this subnet.

Input

The first line contains a subnet in CIDR format.

The second line contains an integer $n$ ($1 \le n \le 1000$), the number of IP addresses to check.

The next $n$ lines each contain an IP address in dotted-decimal notation.

Output

For each of the $n$ lines, output "YES" or "NO" (excluding the quotes) to indicate whether the address belongs to the given subnet.

Examples

Input 1

192.168.88.0/24
5
10.1.1.1
10.2.3.4
192.168.88.0
192.168.88.88
182.168.0.0

Output 1

NO
NO
YES
YES
NO

Input 2

10.0.0.0/16
5
10.0.0.0
10.1.2.3
10.88.88.88
10.0.6.6
172.255.255.255

Output 2

YES
NO
NO
YES
NO

Note

An IPv4 address is a 32-bit binary number, usually composed of four octets. The maximum value that can be represented by an octet is 255 (binary 11111111). Dotted-decimal notation is a format for representing IP addresses, where the four octets of the IP address are separated by dots (.). Each octet is a decimal number between 0 and 255, hence the name dotted-decimal.

An IP address can be divided into a network portion and a host portion by a subnet mask. IP addresses with the same network portion belong to the same subnet. A subnet mask is a 32-bit binary number consisting of a sequence of $1$s followed by a sequence of $0$s, where $1$ represents the network bits and $0$ represents the host bits. For example, 255.255.255.0 (11111111 11111111 11111111 00000000) indicates that the first 24 bits are the network portion and the last 8 bits are the host portion.

CIDR (Classless Inter-Domain Routing) is a simplified and extended way of representing IP addresses, allowing for more flexible definition and allocation of IP addresses and their subnets. CIDR notation is represented by adding a slash '/' followed by a number between 0 and 32 (inclusive) after the IP address to indicate the length of the network portion. This number represents the number of consecutive leading $1$s in the subnet mask.