Problem: In the NN country, there are n cities, numbered from 1 to n, and n - 1 roads, connecting them. There is a roads path between any two cities.

There are m bidirectional bus routes between cities. Buses drive between two cities taking the shortest path with stops in every city they drive through. Travelling by bus, you can travel from any stop on the route to any other. You can travel between cities only by bus.

You are interested in q questions: is it possible to get from one city to another and what is the minimum number of buses you need to use for it?

Input

The first line contains a single integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of cities.

The second line contains n - 1 integers p_2, p_3, …, p_n (1 ≤ p_i < i), where p_i means that cities p_i and i are connected by road.

The third line contains a single integer m (1 ≤ m ≤ 2 ⋅ 10^5) — the number of bus routes.

Each of the next m lines contains 2 integers a and b (1 ≤ a, b ≤ n, a ≠ b), meaning that there is a bus route between cities a and b. It is possible that there is more than one route between two cities.

The next line contains a single integer q (1 ≤ q ≤ 2 ⋅ 10^5) — the number of questions you are interested in.

Each of the next q lines contains 2 integers v and u (1 ≤ v, u ≤ n, v ≠ u), meaning that you are interested if it is possible to get from city v to city u and what is the minimum number of buses you need to use for it.

Output

Print the answer for each question on a separate line. If there is no way to get from one city to another, print -1. Otherwise print the minimum number of buses you have to use.

Examples

Input

7
1 1 1 4 5 6
4
4 2
5 4
1 3
6 7
6
4 5
3 5
7 2
4 5
3 2
5 3


Output

1
3
-1
1
2
3


Input

7
1 1 2 3 4 1
4
4 7
3 5
7 6
7 6
6
4 6
3 1
3 2
2 7
6 3
5 3


Output

1
-1
-1
1
-1
1

Note

<image> Routes for first sample are marked on the picture. 

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class Div1_483E {

	static int nV;
	static ArrayList<Integer>[] chldn;

	static int nR;
	static ArrayList<Integer>[] routes;

	static int nQ;

	static ArrayList<Integer>[] queries;
	static int[][] qInf;

	static boolean[] min1;

	public static void main(String[] args) throws IOException {
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter printer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));

		nV = Integer.parseInt(reader.readLine());

		chldn = new ArrayList[nV];
		routes = new ArrayList[nV];
		queries = new ArrayList[nV];
		for (int i = 0; i < nV; i++) {
			chldn[i] = new ArrayList<>();
			routes[i] = new ArrayList<>();
			queries[i] = new ArrayList<>();
		}

		StringTokenizer inputData = new StringTokenizer(reader.readLine());

		for (int i = 1; i < nV; i++) {
			chldn[Integer.parseInt(inputData.nextToken()) - 1].add(i);
		}

		prepLCA();

		nR = Integer.parseInt(reader.readLine());

		for (int i = 0; i < nR; i++) {
			inputData = new StringTokenizer(reader.readLine());
			int a = Integer.parseInt(inputData.nextToken()) - 1;
			int b = Integer.parseInt(inputData.nextToken()) - 1;
			routes[a].add(b);
			routes[b].add(a);
		}

		prepReach();

		nQ = Integer.parseInt(reader.readLine());
		qInf = new int[nQ][3];
		
		min1 = new boolean[nQ];

		for (int i = 0; i < nQ; i++) {
			inputData = new StringTokenizer(reader.readLine());
			int a = Integer.parseInt(inputData.nextToken()) - 1;
			int b = Integer.parseInt(inputData.nextToken()) - 1;
			int lca = fLCA(a, b);

			int cost = 0;

			for (int k = 16; k >= 0; k--) {
				if (h[reach[a][k]] > h[lca]) {
					a = reach[a][k];
					cost += 1 << k;
				}
			}

			for (int k = 16; k >= 0; k--) {
				if (h[reach[b][k]] > h[lca]) {
					b = reach[b][k];
					cost += 1 << k;
				}
			}

			if (h[reach[a][0]] <= h[lca] && h[reach[b][0]] <= h[lca]) {
				
				if (lca == a || lca == b) {
					qInf[i][2] = cost;
					min1[i] = true;
					continue;
				}
				
				qInf[i][0] = a;
				qInf[i][1] = b;
				qInf[i][2] = cost;
				queries[a].add(i);
				queries[b].add(i);
			} else {
				qInf[i][2] = -1;
			}
		}

		first = new int[nV];
		last = new int[nV];
		BIT = new int[2 * nV + 1];

		eulerDFS(0);


		queryDFS(0);

		for (int i = 0; i < nQ; i++) {
			if (qInf[i][2] == -1) {
				printer.println(-1);
				continue;
			}
			if (min1[i]) {
				printer.println(qInf[i][2] + 1);
			} else {
				printer.println(qInf[i][2] + 2);
			}
		}
		printer.close();
	}

	static void queryDFS(int cV) {
		int[] stores = new int[queries[cV].size()];
		for (int qI = 0; qI < queries[cV].size(); qI++) {
			int cQ = queries[cV].get(qI);
			int eV;
			if (qInf[cQ][0] == cV) {
				eV = qInf[cQ][1];
			} else {
				assert (qInf[cQ][1] == cV);
				eV = qInf[cQ][0];
			}
			stores[qI] = BIT_query(last[eV]) - BIT_query(first[eV] - 1);
		}
		for (int aV : routes[cV]) {
			BIT_add(first[aV], 1);
		}

		for (int aV : chldn[cV]) {
			queryDFS(aV);
		}

		for (int qI = 0; qI < queries[cV].size(); qI++) {
			int cQ = queries[cV].get(qI);
			int eV;
			if (qInf[cQ][0] == cV) {
				eV = qInf[cQ][1];
			} else {
				assert (qInf[cQ][1] == cV);
				eV = qInf[cQ][0];
			}
			if (stores[qI] < BIT_query(last[eV]) - BIT_query(first[eV] - 1)) {
				min1[cQ] = true;
			}
		}
	}

	static int nN = 1;
	static int[] first;
	static int[] last;

	static void eulerDFS(int cV) {
		first[cV] = nN++;
		for (int aV : chldn[cV]) {
			eulerDFS(aV);
		}
		last[cV] = nN++;
	}

	static int[] BIT;

	static void BIT_add(int i, int d) {
		while (i <= 2 * nV) {
			BIT[i] += d;
			i += (i & -i);
		}
	}

	static int BIT_query(int i) {
		int sum = 0;
		while (i > 0) {
			sum += BIT[i];
			i -= (i & -i);
		}
		return sum;
	}

	static int[] h;
	static int[][] anc;

	static void lcaDFS(int cV) {
		for (int aV : chldn[cV]) {
			h[aV] = h[cV] + 1;
			anc[aV][0] = cV;
			lcaDFS(aV);
		}
	}

	static void prepLCA() {
		h = new int[nV];
		anc = new int[nV][17];
		lcaDFS(0);

		for (int k = 1; k < 17; k++) {
			for (int i = 0; i < nV; i++) {
				anc[i][k] = anc[anc[i][k - 1]][k - 1];
			}
		}
	}

	static int fLCA(int a, int b) {
		if (h[a] < h[b]) {
			int t = a;
			a = b;
			b = t;
		}
		int d = h[a] - h[b];
		for (int i = 0; i < 17; i++) {
			if ((d & (1 << i)) != 0) {
				a = anc[a][i];
			}
		}
		if (a == b) {
			return a;
		}
		for (int i = 16; i >= 0; i--) {
			if (anc[a][i] != anc[b][i]) {
				a = anc[a][i];
				b = anc[b][i];
			}
		}
		return anc[a][0];
	}

	static int[][] reach;

	static void prepReach() {
		reach = new int[nV][17];
		for (int i = 0; i < nV; i++) {
			reach[i][0] = i;
		}

		for (int i = 0; i < nV; i++) {
			for (int j : routes[i]) {
				int lca = fLCA(i, j);
				if (h[lca] < h[reach[i][0]]) {
					reach[i][0] = lca;
				}
			}
		}

		reachDFS(0);

		for (int k = 1; k < 17; k++) {
			for (int i = 0; i < nV; i++) {
				reach[i][k] = reach[reach[i][k - 1]][k - 1];
			}
		}
	}

	static void reachDFS(int cV) {
		for (int aV : chldn[cV]) {
			reachDFS(aV);
			if (h[reach[aV][0]] < h[reach[cV][0]]) {
				reach[cV][0] = reach[aV][0];
			}
		}
	}

}