Evlampiy was gifted a rooted tree. The vertices of the tree are numbered from 1 to n. Each of its vertices also has an integer a_i written on it. For each vertex i, Evlampiy calculated c_i — the number of vertices j in the subtree of vertex i, such that a_j < a_i. 

<image>Illustration for the second example, the first integer is a_i and the integer in parentheses is c_i

After the new year, Evlampiy could not remember what his gift was! He remembers the tree and the values of c_i, but he completely forgot which integers a_i were written on the vertices.

Help him to restore initial integers!

Input

The first line contains an integer n (1 ≤ n ≤ 2000) — the number of vertices in the tree.

The next n lines contain descriptions of vertices: the i-th line contains two integers p_i and c_i (0 ≤ p_i ≤ n; 0 ≤ c_i ≤ n-1), where p_i is the parent of vertex i or 0 if vertex i is root, and c_i is the number of vertices j in the subtree of vertex i, such that a_j < a_i.

It is guaranteed that the values of p_i describe a rooted tree with n vertices.

Output

If a solution exists, in the first line print "YES", and in the second line output n integers a_i (1 ≤ a_i ≤ {10}^{9}). If there are several solutions, output any of them. One can prove that if there is a solution, then there is also a solution in which all a_i are between 1 and 10^9.

If there are no solutions, print "NO".

Examples

Input


3
2 0
0 2
2 0


Output


YES
1 2 1 

Input


5
0 1
1 3
2 1
3 0
2 0


Output


YES
2 3 2 1 2
import java.util.*;
import java.io.*;
import java.math.BigInteger;

public class E {
	FastScanner in;
	PrintWriter out;
	boolean systemIO = true;

	public class DSU {
		int[] sz;
		int[] p;

		public DSU(int n) {
			sz = new int[n];
			p = new int[n];
			for (int i = 0; i < p.length; i++) {
				p[i] = i;
				sz[i] = 1;
			}
		}

		public int get(int x) {
			if (x == p[x]) {
				return x;
			}
			int par = get(p[x]);
			p[x] = par;
			return par;
		}

		public boolean unite(int a, int b) {
			int pa = get(a);
			int pb = get(b);
			if (sz[pa] == 1) {
				p[pa] = pb;
				sz[pb] += sz[pa];
				return true;
			}
			if (sz[pb] == 1) {
				p[pb] = pa;
				sz[pa] += sz[pb];
				return true;
			}
			return false;
		}
	}

	public class SegmentTree {
		int pow;
		long[] sum;

		public SegmentTree(long[] a) {
			pow = 1;
			while (pow < a.length) {
				pow *= 2;
			}
			sum = new long[2 * pow];
			for (int i = 0; i < a.length; i++) {
				sum[pow + i] = a[i];
			}
			for (int i = pow - 1; i > 0; i--) {
				sum[i] = f(sum[2 * i], sum[2 * i + 1]);
			}
		}

		public long get(int v, int tl, int tr, int l, int r) {
			if (l > r) {
				return 0;
			}
			if (l == tl && r == tr) {
				return sum[v];
			}
			int tm = (tl + tr) / 2;
			return f(get(2 * v, tl, tm, l, Math.min(r, tm)), get(2 * v + 1, tm + 1, tr, Math.max(l, tm + 1), r));
		}

		public void set(int v, int tl, int tr, int l, int r, long x) {
			if (l > tr || r < tl) {
				return;
			}
			if (l <= tl && r >= tr) {
				return;
			}
			int tm = (tl + tr) / 2;
			set(2 * v, tl, tm, l, r, x);
			set(2 * v + 1, tm + 1, tr, l, r, x);
			sum[v] = f(sum[2 * v], sum[2 * v + 1]);
		}

		public long f(long a, long b) {
			return a + b;
		}
	}

	public class SegmentTreeAdd {
		int pow;
		long[] sum;
		long[] delta;
		boolean[] flag;

		public SegmentTreeAdd(long[] a) {
			pow = 1;
			while (pow < a.length) {
				pow *= 2;
			}
			flag = new boolean[2 * pow];
			sum = new long[2 * pow];
			delta = new long[2 * pow];
			for (int i = 0; i < a.length; i++) {
				sum[pow + i] = a[i];
			}
			for (int i = pow - 1; i > 0; i--) {
				sum[i] = f(sum[2 * i], sum[2 * i + 1]);
			}
		}

		public long get(int v, int tl, int tr, int l, int r) {
			push(v, tl, tr);
			if (l > r) {
				return 0;
			}
			if (l == tl && r == tr) {
				return sum[v];
			}
			int tm = (tl + tr) / 2;
			return f(get(2 * v, tl, tm, l, Math.min(r, tm)), get(2 * v + 1, tm + 1, tr, Math.max(l, tm + 1), r));
		}

		public void set(int v, int tl, int tr, int l, int r, long x) {
			push(v, tl, tr);
			if (l > tr || r < tl) {
				return;
			}
			if (l <= tl && r >= tr) {
				delta[v] += x;
				flag[v] = true;
				push(v, tl, tr);
				return;
			}
			int tm = (tl + tr) / 2;
			set(2 * v, tl, tm, l, r, x);
			set(2 * v + 1, tm + 1, tr, l, r, x);
			sum[v] = f(sum[2 * v], sum[2 * v + 1]);
		}

		public void push(int v, int tl, int tr) {
			if (flag[v]) {
				if (v < pow) {
					flag[2 * v] = true;
					flag[2 * v + 1] = true;
					delta[2 * v] += delta[v];
					delta[2 * v + 1] += delta[v];
				}
				flag[v] = false;
				sum[v] += delta[v] * (tr - tl + 1);
			}
		}

		public long f(long a, long b) {
			return a + b;
		}
	}

	public class SegmentTreeSet {
		int pow;
		int[] sum;
		int[] delta;
		boolean[] flag;

		public SegmentTreeSet(int[] a) {
			pow = 1;
			while (pow < a.length) {
				pow *= 2;
			}
			flag = new boolean[2 * pow];
			sum = new int[2 * pow];
			delta = new int[2 * pow];
			for (int i = 0; i < a.length; i++) {
				sum[pow + i] = a[i];
			}
		}

		public int get(int v, int tl, int tr, int l, int r) {
			push(v, tl, tr);
			if (l > r) {
				return 0;
			}
			if (l == tl && r == tr) {
				return sum[v];
			}
			int tm = (tl + tr) / 2;
			return f(get(2 * v, tl, tm, l, Math.min(r, tm)), get(2 * v + 1, tm + 1, tr, Math.max(l, tm + 1), r));
		}

		public void set(int v, int tl, int tr, int l, int r, int x) {
			push(v, tl, tr);
			if (l > tr || r < tl) {
				return;
			}
			if (l <= tl && r >= tr) {
				delta[v] = x;
				flag[v] = true;
				push(v, tl, tr);
				return;
			}
			int tm = (tl + tr) / 2;
			set(2 * v, tl, tm, l, r, x);
			set(2 * v + 1, tm + 1, tr, l, r, x);
			sum[v] = f(sum[2 * v], sum[2 * v + 1]);
		}

		public void push(int v, int tl, int tr) {
			if (flag[v]) {
				if (v < pow) {
					flag[2 * v] = true;
					flag[2 * v + 1] = true;
					delta[2 * v] = delta[v];
					delta[2 * v + 1] = delta[v];
				}
				flag[v] = false;
				sum[v] = delta[v] * (tr - tl + 1);
			}
		}

		public int f(int a, int b) {
			return a + b;
		}
	}

	public class Pair implements Comparable<Pair> {
		int x;
		int y;

		public Pair(int x, int y) {
			this.x = x;
			this.y = y;
		}

		public Pair clone() {
			return new Pair(x, y);
		}

		public String toString() {
			return x + " " + y;
		}

		@Override
		public int compareTo(Pair o) {
			if (x > o.x) {
				return 1;
			}
			if (x < o.x) {
				return -1;
			}
			return -(y - o.y);
		}
	}

	long mod;
	Random random = new Random();

	public void shuffle(Pair[] a) {
		for (int i = 0; i < a.length; i++) {
			int x = random.nextInt(i + 1);
			Pair t = a[x];
			a[x] = a[i];
			a[i] = t;
		}
	}

	public void sort(int[][] a) {
		for (int i = 0; i < a.length; i++) {
			Arrays.sort(a[i]);
		}
	}

	public static class Fenvik {
		long[] t;

		public Fenvik(int n) {
			t = new long[n];
		}

		public void add(int x, long delta) {
			for (int i = x; i < t.length; i = (i | (i + 1))) {
				t[i] += delta;
			}
		}

		private long sum(int r) {
			long ans = 0;
			int x = r;
			while (x >= 0) {
				ans += t[x];
				x = (x & (x + 1)) - 1;
			}
			return ans;
		}

		public long sum(int l, int r) {
			return sum(r) - sum(l - 1);
		}
	}

	public int gcd(int x, int y) {
		if (x == 0) {
			return y;
		}
		return gcd(y % x, x);
	}

	public class Vector {
		int x;
		int y;

		public Vector(int x, int y) {
			this.x = x;
			this.y = y;
		}

		public Vector add(Vector v) {
			return new Vector(x + v.x, y + v.y);
		}
	}

	public long cp(Vector v0, Vector v1, Vector v2) {
		return (v1.x - v0.x) * (v2.y - v0.y) - (v1.y - v0.y) * (v2.x - v0.x);
	}

	public int dfsSz(int v) {
		for (int i : to[v]) {
			sz[v] += dfsSz(i);
		}
		return sz[v] + 1;
	}
	
	public boolean dfs(int v) {
		if (c[v] > sz[v]) {
			return false;
		}
		a[v] = number.get(c[v]);
		number.remove(c[v]);
		for (int i : to[v]) {
			if (!dfs(i)) {
				return false;
			}
		}
		return true;
	}
	
	ArrayList<Integer>[] to;
	ArrayList<Integer> number = new ArrayList<>();
	int[] c;
	int[] a;
	int[] sz;
	int root = -1;
	
	@SuppressWarnings("unchecked")
	public void solve() {
		int n = in.nextInt();
		to = new ArrayList[n];
		for (int i = 0; i < to.length; i++) {
			to[i] = new ArrayList<>();
		}
		c = new int[n];
		a = new int[n];
		sz = new int[n];
		for (int i = 1; i <= n; i++) {
			number.add(i);
		}
		for (int i = 0; i < n; i++) {
			int from = in.nextInt() - 1;
			if (from < 0) {
				root = i;
			} else {
				to[from].add(i);
			}
			c[i] = in.nextInt();
		}
		dfsSz(root);
		if (dfs(root)) {
			out.println("YES");
			for (int i = 0; i < a.length; i++) {
				out.print(a[i] + " ");
			}
		} else {
			out.println("NO");
		}
	}

	public void run() {
		try {
			if (systemIO) {
				in = new FastScanner(System.in);
				out = new PrintWriter(System.out);
			} else {
				in = new FastScanner(new File("frequent.in"));
				out = new PrintWriter(new File("frequent.out"));
			}
			solve();

			out.close();
		} catch (IOException e) {
			e.printStackTrace();
		}
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		FastScanner(File f) {
			try {
				br = new BufferedReader(new FileReader(f));
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
		}

		FastScanner(InputStream f) {
			br = new BufferedReader(new InputStreamReader(f));
		}

		String nextLine() {
			try {
				return br.readLine();
			} catch (IOException e) {
				return null;
			}
		}

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

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

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

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

	}

	// AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
	public static void main(String[] arg) {
		new E().run();
	}
}