Problem: Gardener Alex loves to grow trees. We remind that tree is a connected acyclic graph on n vertices. 

Today he decided to grow a rooted binary tree. A binary tree is a tree where any vertex has no more than two sons. Luckily, Alex has a permutation of numbers from 1 to n which he was presented at his last birthday, so he decided to grow a tree according to this permutation. To do so he does the following process: he finds a minimum element and makes it a root of the tree. After that permutation is divided into two parts: everything that is to the left of the minimum element, and everything that is to the right. The minimum element on the left part becomes the left son of the root, and the minimum element on the right part becomes the right son of the root. After that, this process is repeated recursively on both parts.

Now Alex wants to grow a forest of trees: one tree for each cyclic shift of the permutation. He is interested in what cyclic shift gives the tree of minimum depth. Unfortunately, growing a forest is a hard and long process, but Alex wants the answer right now. Will you help him?

We remind that cyclic shift of permutation a_1, a_2, …, a_k, …, a_n for k elements to the left is the permutation a_{k + 1}, a_{k + 2}, …, a_n, a_1, a_2, …, a_k.

Input

First line contains an integer number n ~ (1 ⩽ n ⩽ 200 000) — length of the permutation.

Second line contains n integer numbers a_1, a_2, …, a_n ~ (1 ⩽ a_i ⩽ n), and it is guaranteed that all numbers occur exactly one time.

Output

Print two numbers separated with space: minimum possible depth of a tree and how many elements we need to shift left to achieve this depth. The number of elements should be a number from 0 to n - 1. If there are several possible answers, print any of them.

Example

Input


4
1 2 3 4


Output


3 2

Note

The following picture depicts all possible trees for sample test and cyclic shifts on which they are achieved. 

<image>

Solution (in JAVA):

Solution:
import java.io.ByteArrayInputStream;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.nio.charset.StandardCharsets;
import java.util.Arrays;
import java.util.InputMismatchException;

public class F1220 {
	static class Solver {

		int N, perm[], firstLeft[], firstRight[];
		Node st; RMQ RMQ;
		
		void solve(int testNumber, FastScanner s, PrintWriter out) {
			N = s.nextInt(); perm = new int[N << 1];
			firstLeft = new int[N << 1]; firstRight = new int[N << 1];
			for(int i = 0; i < N; i++) perm[i] = perm[i + N] = s.nextInt();
			st = new Node(0, 2 * N - 1);
			RMQ = new RMQ(perm);

			int lo, hi, m, f, v;
			for(int i = 0; i < 2 * N; i++) {
				lo = 1; hi = i; f = i + 1; v = perm[i];
				while(lo <= hi) {
					m = lo + (hi - lo) / 2;
					if(RMQ.query(i - m, i - 1) <= v) {
						f = m; hi = m - 1;
					} else {
						lo = m + 1;
					}
				}
				firstLeft[i] = i - f + 1;
				lo = 1; hi = 2 * N - i - 1; f = 2 * N;
				while(lo <= hi) {
					m = lo + (hi - lo) / 2;
					if(RMQ.query(i + 1, i + m) <= v) {
						f = m; hi = m - 1;
					} else {
						lo = m + 1;
					}
				}
				firstRight[i] = i + f - 1;
			}

			for (int i = 0; i < N; i++) st.add(firstLeft[i], firstRight[i], 1);

			int mindepth = 69_420_1337, shift = -1;
			for(int l = 0, r = N - 1; l < N; l++, r++) {
				int cd = st.max(l, r);
				if(cd < mindepth) {
					mindepth = cd; shift = l;
				}
				st.add(firstLeft[l], firstRight[l], -1);
				if(r != 2 * N - 1) st.add(firstLeft[r + 1], firstRight[r + 1], 1);
			}
			out.printf("%d %d%n", mindepth, shift);
		}
		
		class Node {
			int l, m, r, lz, max, mn;
			Node L, R;
			Node(int ll, int rr) {
				l = ll; r = rr; m = l + (r - l) / 2;
				lz = max = 0;
				if(l == r) return;
				L = new Node(l, m); R = new Node(m + 1, r);
				mn = L.mn < R.mn ? L.mn : R.mn;
			}
			
			void push() {
				if(lz != 0) {
					L.add(l, r, lz); R.add(l, r, lz);
					max = L.max > R.max ? L.max : R.max;
				} lz = 0;
			}
			
			void add(int s, int e, int x) {
				if(s <= l && r <= e) {
					lz += x; max += x; return;
				}
				push();
				if(s <= m) L.add(s, e, x);
				if(m < e) R.add(s, e, x);
				max = L.max > R.max ? L.max : R.max;
			}
			
			int max(int s, int e) {
				if(s <= l && r <= e) { return max; }
				push();
				int mx = 0;
				if(s <= m) mx = Math.max(mx, L.max(s, e));
				if(m < e) mx = Math.max(mx, R.max(s, e));
				return mx;
			}
		}
		
		static class RMQ {
			int[] vs;
			int[][] lift;

			public RMQ(int[] vs) {
				this.vs = vs;
				int n = vs.length;
				int maxlog = Integer.numberOfTrailingZeros(Integer.highestOneBit(n)) + 2;
				lift = new int[maxlog][n];
				for (int i = 0; i < n; i++)
					lift[0][i] = vs[i];
				int lastRange = 1;
				for (int lg = 1; lg < maxlog; lg++) {
					for (int i = 0; i < n; i++) {
						lift[lg][i] = Math.min(lift[lg - 1][i], lift[lg - 1][Math.min(i + lastRange, n - 1)]);
					}
					lastRange *= 2;
				}
			}

			public int query(int low, int hi) {
				int range = hi - low + 1;
				int exp = Integer.highestOneBit(range);
				int lg = Integer.numberOfTrailingZeros(exp);
				return Math.min(lift[lg][low], lift[lg][hi - exp + 1]);
			}
		}

	}

	final static boolean cases = false;

	public static void main(String[] args) {

		FastScanner s = new FastScanner(System.in);
		PrintWriter out = new PrintWriter(System.out);

		Solver solver = new Solver();
		for (int t = 1, T = cases ? s.nextInt() : 1; t <= T; t++)
			solver.solve(t, s, out);

		out.close();

	}

	static int min(int a, int b) {
		return a < b ? a : b;
	}

	static int max(int a, int b) {
		return a > b ? a : b;
	}

	static long min(long a, long b) {
		return a < b ? a : b;
	}

	static long max(long a, long b) {
		return a > b ? a : b;
	}

	static int swap(int a, int b) {
		return a;
	}

	static Object swap(Object a, Object b) {
		return a;
	}

	static String ts(Object... o) {
		return Arrays.deepToString(o);
	}

	static class FastScanner {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

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

		public FastScanner(File f) throws FileNotFoundException {
			this(new FileInputStream(f));
		}

		public FastScanner(String s) {
			this.stream = new ByteArrayInputStream(s.getBytes(StandardCharsets.UTF_8));
		}

		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++];
		}

		boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		boolean isEndline(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public String next() {
			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 String nextLine() {
			int c = read();
			while (isEndline(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndline(c));
			return res.toString();
		}

		// Jacob Garbage

		public int[] nextIntArray(int N) {
			int[] ret = new int[N];
			for (int i = 0; i < N; i++)
				ret[i] = this.nextInt();
			return ret;
		}

		public int[][] next2DIntArray(int N, int M) {
			int[][] ret = new int[N][];
			for (int i = 0; i < N; i++)
				ret[i] = this.nextIntArray(M);
			return ret;
		}

		public long[] nextLongArray(int N) {
			long[] ret = new long[N];
			for (int i = 0; i < N; i++)
				ret[i] = this.nextLong();
			return ret;
		}

		public long[][] next2DLongArray(int N, int M) {
			long[][] ret = new long[N][];
			for (int i = 0; i < N; i++)
				ret[i] = nextLongArray(M);
			return ret;
		}

		public double[] nextDoubleArray(int N) {
			double[] ret = new double[N];
			for (int i = 0; i < N; i++)
				ret[i] = this.nextDouble();
			return ret;
		}

		public double[][] next2DDoubleArray(int N, int M) {
			double[][] ret = new double[N][];
			for (int i = 0; i < N; i++)
				ret[i] = this.nextDoubleArray(M);
			return ret;
		}

	}
}