Ridbit starts with an integer n.

In one move, he can perform one of the following operations: 

  * divide n by one of its proper divisors, or 
  * subtract 1 from n if n is greater than 1. 



A proper divisor is a divisor of a number, excluding itself. For example, 1, 2, 4, 5, and 10 are proper divisors of 20, but 20 itself is not.

What is the minimum number of moves Ridbit is required to make to reduce n to 1?

Input

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases.

The only line of each test case contains a single integer n (1 ≤ n ≤ 10^9).

Output

For each test case, output the minimum number of moves required to reduce n to 1.

Example

Input


6
1
2
3
4
6
9


Output


0
1
2
2
2
3

Note

For the test cases in the example, n may be reduced to 1 using the following operations in sequence

1

2 \xrightarrow{} 1

3 \xrightarrow{} 2 \xrightarrow{} 1

4 \xrightarrow{} 2 \xrightarrow{} 1

6 \xrightarrow{} 2 \xrightarrow{} 1

9 \xrightarrow{} 3 \xrightarrow{} 2\xrightarrow{} 1
from fractions import Fraction
import bisect
import os
import io
from collections import Counter
import bisect
from collections import defaultdict
import math
import random
import heapq
from math import sqrt
import sys
from functools import reduce, cmp_to_key
from collections import deque
import threading
from itertools import combinations
from io import BytesIO, IOBase
from itertools import accumulate
from queue import Queue


# sys.setrecursionlimit(200000)
# input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline


def input():
    return sys.stdin.readline().strip()


def iinput():
    return int(input())


def tinput():
    return input().split()


def rinput():
    return map(int, tinput())


def rlinput():
    return list(rinput())


mod = int(1e9)+7


def factors(n):
    return set(reduce(list.__add__,
                      ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0)))


# ----------------------------------------------------
# sys.stdin = open('input.txt', 'r')
# sys.stdout = open('output.txt', 'w')


# ----------------------------------------------------------------


t = iinput()
# t  = 1
for _ in range(t):
    n = iinput()
    if n == 1:
        print(0)
    elif n == 2:
        print(1)
    elif n == 3:
        print(2)
    else:
        print(3 if n%2 else 2)
