Problem:
Score : 900 points

Problem Statement

Let x be a string of length at least 1.
We will call x a good string, if for any string y and any integer k (k \geq 2), the string obtained by concatenating k copies of y is different from x.
For example, a, bbc and cdcdc are good strings, while aa, bbbb and cdcdcd are not.

Let w be a string of length at least 1.
For a sequence F=(\,f_1,\,f_2,\,...,\,f_m) consisting of m elements,
we will call F a good representation of w, if the following conditions are both satisfied:

For any i \, (1 \leq i \leq m), f_i is a good string.

The string obtained by concatenating f_1,\,f_2,\,...,\,f_m in this order, is w.

For example, when w=aabb, there are five good representations of w:

(aabb)

(a,abb)

(aab,b)

(a,ab,b)

(a,a,b,b)

Among the good representations of w, the ones with the smallest number of elements are called the best representations of w.
For example, there are only one best representation of w=aabb: (aabb).

You are given a string w. Find the following:

the number of elements of a best representation of w

the number of the best representations of w, modulo 1000000007 \, (=10^9+7)

(It is guaranteed that a good representation of w always exists.)

Constraints

1 \leq |w| \leq 500000 \, (=5 \times 10^5)

w consists of lowercase letters (a-z).

Partial Score

400 points will be awarded for passing the test set satisfying 1 \leq |w| \leq 4000.

Input

The input is given from Standard Input in the following format:

w

Output

Print 2 lines.

In the first line, print the number of elements of a best representation of w.

In the second line, print the number of the best representations of w, modulo 1000000007.

Sample Input 1

aab

Sample Output 1

1
1

Sample Input 2

bcbc

Sample Output 2

2
3

In this case, there are 3 best representations of 2 elements:

(b,cbc)

(bc,bc)

(bcb,c)

Sample Input 3

ddd

Sample Output 3

3
1

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;

public class Main {
	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";

	public static void main(String[] args) throws Exception {
		new Main().run();
	}

	void solver(char[] w) {
		boolean all = true;
		for (int i = 1; i < w.length; i++) {
			if (w[i] != w[i - 1]) {
				all = false;
				break;
			}
		}
		if (all) {
			out.println(w.length + "\n" + 1);
			return;
		}
		int n = w.length;
		long b = 29;
		long[] mod = { 1000000007 };
		hash = new long[mod.length][n];
		pow = new long[mod.length][n];
		for (int i = 0; i < 1; i++) {
			for (int j = 0; j < n; j++) {
				if (j == 0)
					pow[i][j] = 1;
				else {
					pow[i][j] = pow[i][j - 1] * b;
					if (pow[i][j] >= mod[i])
						pow[i][j] %= mod[i];
				}
			}
		}

		for (int i = 0; i < 1; i++) {
			for (int j = n - 1; j >= 0; j--) {
				hash[i][j] = (w[j] - 'a') + (j == n - 1 ? 0 : hash[i][j + 1] * b);
				if (hash[i][j] >= mod[i])
					hash[i][j] %= mod[i];
			}
		}
		div = new ArrayList[n + 1];
		for (int i = 0; i <= n; i++) {
			div[i] = new ArrayList<>();
			if (i > 1)
				div[i].add(1);
		}
		for (int i = n - 1; i >= 1; i--) {
			for (long j = 2L * i; j <= n; j += i) {
				div[(int) j].add(i);
			}
		}
		for (int i = 0; i < 1; i++) {
			if (isGood(0, n, mod[i], i)) {
				out.println("1\n1");
				return;
			}
		}
		long ret = 0;
		ok = new boolean[n];
		Arrays.fill(ok, true);
		for (int i = 1; i < n; i++) {
			boolean f = true;
			for (int j = 0; j < 1; j++) {
				if (!ok[i] || !isGood(i, n, mod[j], j) || !isGood(0, i, mod[j], j)) {
					f = false;
					break;
				}
			}
			if (f) {
				ret++;
			}
		}
		out.println(2 + "\n" + ret);
	}

	ArrayList<Integer>[] div;
	boolean[] ok;
	long[][] hash;
	long[][] pow;

	boolean isGood(int s, int t, long mod, int mode) {
		for (int period : div[t - s]) {
			long v1 = (hash[mode][s] - hash[mode][t - period] * pow[mode][t - s - period] % mod + mod) % mod;
			long v2 = (hash[mode][s + period]
					- (t == hash[mode].length ? 0 : hash[mode][t] * pow[mode][t - s - period] % mod) + mod) % mod;
			if (v1 == v2) {
				if (s != 0) {
					for (int j = s + period; j + 2 * period <= t; j += period) {
						ok[j] = false;
					}
				}
				return false;
			}
		}
		return true;
	}

	void run() {
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		solver(ns().toCharArray());
		out.flush();
	}

	char[] gen() {
		int n = (int) (1 + Math.random() * 500000);
		char[] c = new char[n];
		for (int i = 0; i < n; i++) {
			c[i] = (char) ('a' + (int) (Math.random() * 2));
		}
		tr(c);
		return c;
	}

	static long nl() {
		try {
			long num = 0;
			boolean minus = false;
			while ((num = is.read()) != -1 && !((num >= '0' && num <= '9') || num == '-'))
				;
			if (num == '-') {
				num = 0;
				minus = true;
			} else {
				num -= '0';
			}

			while (true) {
				int b = is.read();
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
			}
		} catch (IOException e) {
		}
		return -1;
	}

	static char nc() {
		try {
			int b = skip();
			if (b == -1)
				return 0;
			return (char) b;
		} catch (IOException e) {
		}
		return 0;
	}

	static double nd() {
		try {
			return Double.parseDouble(ns());
		} catch (Exception e) {
		}
		return 0;
	}

	static String ns() {
		try {
			int b = skip();
			StringBuilder sb = new StringBuilder();
			if (b == -1)
				return "";
			sb.append((char) b);
			while (true) {
				b = is.read();
				if (b == -1)
					return sb.toString();
				if (b <= ' ')
					return sb.toString();
				sb.append((char) b);
			}
		} catch (IOException e) {
		}
		return "";
	}

	public static char[] ns(int n) {
		char[] buf = new char[n];
		try {
			int b = skip(), p = 0;
			if (b == -1)
				return null;
			buf[p++] = (char) b;
			while (p < n) {
				b = is.read();
				if (b == -1 || b <= ' ')
					break;
				buf[p++] = (char) b;
			}
			return Arrays.copyOf(buf, p);
		} catch (IOException e) {
		}
		return null;
	}

	public static byte[] nse(int n) {
		byte[] buf = new byte[n];
		try {
			int b = skip();
			if (b == -1)
				return null;
			is.read(buf);
			return buf;
		} catch (IOException e) {
		}
		return null;
	}

	static int skip() throws IOException {
		int b;
		while ((b = is.read()) != -1 && !(b >= 33 && b <= 126))
			;
		return b;
	}

	static boolean eof() {
		try {
			is.mark(1000);
			int b = skip();
			is.reset();
			return b == -1;
		} catch (IOException e) {
			return true;
		}
	}

	static int ni() {
		try {
			int num = 0;
			boolean minus = false;
			while ((num = is.read()) != -1 && !((num >= '0' && num <= '9') || num == '-'))
				;
			if (num == '-') {
				num = 0;
				minus = true;
			} else {
				num -= '0';
			}

			while (true) {
				int b = is.read();
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
			}
		} catch (IOException e) {
		}
		return -1;
	}

	static void tr(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}
}