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
import java.io.*;
import java.util.*;
import java.math.*;
import java.lang.*;

public class Main implements Runnable {
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();

            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }

                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        public int nextInt() {
            int c = read();

            while (isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-') {
                sgn = -1;
                c = read();
            }

            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));

            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;

            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    public static void main(String args[]) throws Exception {
        new Thread(null, new Main(), "Main", 1 << 27).start();
    }

    static class Pair {
        int f;
        int s;
        PrintWriter w;

        // int t;

        Pair(int f, int s) {
            // Pair(int f,int s, PrintWriter w){
            this.f = f;
            this.s = s;
            // this.w = w;
            // this.t = t;

        }

        public static Comparator<Pair> wc = new Comparator<Pair>() {
            public int compare(Pair e1, Pair e2) {

                // 1 for swap
                if (Math.abs(e1.f) - Math.abs(e2.f) != 0) {
                    // e1.w.println("**"+e1.f+" "+e2.f);
                    return (Math.abs(e1.f) - Math.abs(e2.f));
                } else {
                    // e1.w.println("##"+e1.f+" "+e2.f);
                    return (Math.abs(e1.s) - Math.abs(e2.s));
                }

            }
        };
    }

    public static long gcd(long a, long b) {
        if (b == 0)
            return a;
        else
            return gcd(b, a % b);
    }

    //// recursive BFS
    public static int bfsr(int s, ArrayList<Integer>[] a, boolean[] b, int[] pre) {
        b[s] = true;
        int p = 1;
        int n = pre.length - 1;
        int t = a[s].size();
        int max = 1;
        for (int i = 0; i < t; i++) {
            int x = a[s].get(i);
            if (!b[x]) {
                // dist[x] = dist[s] + 1;
                int xz = (bfsr(x, a, b, pre));
                p += xz;
                max = Math.max(xz, max);
            }
        }
        // max = Math.max(max,(n-p));
        pre[s] = max;
        return p;
    }

    //// iterative BFS
    public static int bfs(int s, ArrayList<Integer>[] a, int dist, boolean[] b, PrintWriter w) {
        b[s] = true;
        int siz = 0;
        dist--;
        Queue<Integer> q = new LinkedList<>();
        q.add(s);
        while (q.size() != 0 && dist > 0) {
            int i = q.poll();
            Iterator<Integer> it = a[i].listIterator();
            int z = 0;
            while (it.hasNext() && dist > 0) {
                z = it.next();
                if (!b[z]) {
                    b[z] = true;
                    dist--;
                    // dist[z] = dist[i] + 1;
                    siz++;
                    q.add(z);
                }
            }

        }
        return siz;
    }

    public static int lower(int key, Integer[] a) {
        int l = 0;
        int r = a.length - 1;
        int res = 0;

        while (l <= r) {
            int mid = (l + r) / 2;

            if (a[mid] <= key) {
                l = mid + 1;
                res = mid + 1;
            } else {
                r = mid - 1;
            }
        }

        return res;
    }

    public static long power(long x, long y, long m) {
        if (y == 0)
            return 1;

        long p = power(x, y / 2, m) % m;
        p = (p * p) % m;

        if (y % 2 == 0)
            return p;
        else
            return (x * p) % m;
    }

    //////////////////////////////////////////////////////////////////////////////////////////////////////
    //////////////////////////////////////////////////////////////////////////////////////////////////////

    public void run() {
        // code here
        InputReader sc = new InputReader(System.in);
        PrintWriter w = new PrintWriter(System.out);

        int defaultValue = 0;
        long mod = Long.valueOf("1000000007");

        int tc = sc.nextInt();
        while (tc-- > 0) {
            int n = sc.nextInt();
            int ans = 0;
            if(n%2==0){
                if(n>2)
                w.println(2);
                else
                w.println(1);
            }
            else{
                if(n>1){
                    if(n>3){
                        w.println(3);
                    }
                    else w.println(2);
                }
                else{
                    w.println(0);
                }
            }

        }
        w.flush();
        w.close();

    }

}
