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.io.*;
import java.util.*;


public class tr1 {
	static PrintWriter out;
	static StringBuilder sb;
	static int inf = (int) 1e9;
	static long mod = (long) 998244353;
	static int[] si;
	static ArrayList<Integer> primes;
	static HashSet<Integer> pr;
	static int n, k, m;
	static int[] in;
	static HashMap<Integer, Integer> factors;
	static HashSet<Integer> f;
	static int[] fac, a, b;
	static int[] l, r;
	static int[][] memo;
	static int[] numc;
	static ArrayList<Integer>[] ad;
	static HashMap<Integer, Integer> hm;
	static pair[] ed;
	static TreeSet<Integer>[] np;
	static TreeMap<pair, Integer> tm;
	static int[] le, re;
	static char[] h;
	static pair[] mm;
	static boolean[] vis;
	static int y;

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		out = new PrintWriter(System.out);
		int n=sc.nextInt();
		ad=new ArrayList[n];
		for(int i=0;i<n;i++)
			ad[i]=new ArrayList<>();
		int []v=new int [n];
		int []p=new int [n];
		int root=-1;
		for(int i=0;i<n;i++) {
			int a=sc.nextInt()-1;
			int b=sc.nextInt();
			v[i]=b;
			if(a==-1)
				root=i;
			else {
				ad[a].add(i);
				ad[i].add(a);
				p[i]=a;
			}
		}
		p[root]=-1;
		PriorityQueue<pair> pq=new PriorityQueue<>();
		boolean []vis=new boolean [n];
		int []l=new int [n];
		Queue <Integer> q=new LinkedList();
		q.add(root);
		Arrays.fill(l, -1);
		l[root]=0;
		while(!q.isEmpty()) {
			int cur=q.remove();
		     for(int u:ad[cur])
		    	 if(l[u]==-1) {
		    		 l[u]=1+l[cur];
		    		 q.add(u);
		    	 }
		}
		for(int i=0;i<n;i++)
			if(v[i]==0) {
				pq.add(new pair( i, l[i]));
				vis[i]=true;
			}
		int []ans=new int [n];
		int cu=1;
//		System.out.println(Arrays.toString(l));
		while(!pq.isEmpty()) {
			pair cur=pq.poll();
	//		System.out.println(cur);
			ans[cur.node]=cu++;
			int pa=p[cur.node];
			while(pa!=-1) {
				v[pa]--;
				if(v[pa]==0) {
					pq.add(new pair(pa, l[pa]));
				}
				pa=p[pa];
			}
		}
		for(int i=0;i<n;i++)
			if(ans[i]==0) {
				out.print("NO");
				out.flush();
				return;
			}
		out.println("YES");
		for(int i=0;i<n;i++)
			out.print(ans[i]+" ");
		out.flush();
	}

	static class pair implements Comparable<pair> {
		int node;
		int level;

		pair(int f, int t) {
			node=f;
			level=t;
		}

		public String toString() {
			return node+" "+level;
		}

		@Override
		public int compareTo(pair o) {
			return level - o.level;
		}
	}

	static class pair1 implements Comparable<pair1> {
		int x;
		int y;
		int z;

		pair1(int f, int t, int u) {
			x = f;
			y = t;
			z = u;
			// num = n;
		}

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

		@Override
		public int compareTo(pair1 o) {
			if (x == o.x)
				return y - o.y;
			return x - o.x;
		}
	}

	static public class FenwickTree { // one-based DS

		int n;
		int[] ft;

		FenwickTree(int size) {
			n = size;
			ft = new int[n + 1];
			// for(int i=1;i<=n;i++)
			// ft[i]=i;
		}

		int rsq(int b) // O(log n)
		{
			int sum = 0;
			while (b > 0) {
				sum += ft[b];
				b -= b & -b;
			} // min?
			return sum;
		}

		int rsq(int a, int b) {
			return rsq(b) - rsq(a - 1);
		}

		void point_update(int k, int val) // O(log n), update = increment
		{
			while (k <= n) {
				// System.out.println(k+" "+val);
				ft[k] += val;
				k += k & -k;
			} // min?
		}

		int point_query(int idx) // c * O(log n), c < 1
		{
			int sum = ft[idx];
			if (idx > 0) {
				int z = idx ^ (idx & -idx);
				--idx;
				while (idx != z) {
					// System.out.println("oo");
					sum -= ft[idx];
					idx ^= idx & -idx;
				}
			}
			return sum;
		}

		void scale(int c) {
			for (int i = 1; i <= n; ++i)
				ft[i] *= c;
		}

		int findIndex(int cumFreq) {
			int msk = n;
			while ((msk & (msk - 1)) != 0)
				msk ^= msk & -msk; // msk will contain the MSB of n

			int idx = 0;
			while (msk != 0) {
				int tIdx = idx + msk;
				if (tIdx <= n && cumFreq >= ft[tIdx]) {
					idx = tIdx;
					cumFreq -= ft[tIdx];
				}
				msk >>= 1;
			}
			if (cumFreq != 0)
				return -1;
			return idx;
		}
	}

	static public class SegmentTree { // 1-based DS, OOP

		int N; // the number of elements in the array as a power of 2 (i.e. after padding)
		long[] array, sTree, lazy;

		SegmentTree(long[] in) {
			array = in;
			N = in.length - 1;
			sTree = new long[N << 1]; // no. of nodes = 2*N - 1, we add one to cross out index zero
			lazy = new long[N << 1];
			build(1, 1, N);
		}

		void build(int node, int b, int e) // O(n)
		{
			if (b == e)
				sTree[node] = array[b];
			else {
				int mid = b + e >> 1;
				build(node << 1, b, mid);
				build(node << 1 | 1, mid + 1, e);
				sTree[node] = sTree[node << 1] + sTree[node << 1 | 1];
			}
		}

		void update_point(int index, int val) // O(log n)
		{
			index += N - 1;
			sTree[index] += val;
			while (index > 1) {
				index >>= 1;
				sTree[index] = sTree[index << 1] + sTree[index << 1 | 1];
			}
		}

		void update_range(int i, int j, long val) // O(log n)
		{
			update_range(1, 1, N, i, j, val);
		}

		void update_range(int node, int b, int e, int i, int j, long val) {
			if (i > e || j < b)
				return;
			if (b >= i && e <= j) {
				sTree[node] += (e - b + 1) * val;
				lazy[node] += val;
			} else {
				int mid = b + e >> 1;
				propagate(node, b, mid, e);
				update_range(node << 1, b, mid, i, j, val);
				update_range(node << 1 | 1, mid + 1, e, i, j, val);
				sTree[node] = sTree[node << 1] + sTree[node << 1 | 1];
			}

		}

		void propagate(int node, int b, int mid, int e) {
			lazy[node << 1] += lazy[node];
			lazy[node << 1 | 1] += lazy[node];
			sTree[node << 1] += (mid - b + 1) * lazy[node];
			sTree[node << 1 | 1] += (e - mid) * lazy[node];
			lazy[node] = 0;
		}

		long query(int i, int j) {
			return query(1, 1, N, i, j);
		}

		long query(int node, int b, int e, int i, int j) // O(log n)
		{
			if (i > e || j < b)
				return 0;
			if (b >= i && e <= j)
				return sTree[node];
			int mid = b + e >> 1;
			propagate(node, b, mid, e);
			long q1 = query(node << 1, b, mid, i, j);
			long q2 = query(node << 1 | 1, mid + 1, e, i, j);
			return q1 + q2;

		}

	}

	static long gcd(long a, long b) {

		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}

	public int[] merge(int[] d, int st, int e) {
		if (st > e)
			return null;
		if (e == st) {
			int[] ans = { d[e] };
			return ans;
		}
		int mid = (st + e) / 2;
		int[] ans = new int[e - st + 1];
		int[] ll = merge(d, st, mid);
		int[] rr = merge(d, mid + 1, e);
		if (ll == null)
			return rr;
		if (rr == null)
			return ll;
		int iver = 0;
		int idxl = 0;
		int idxr = 0;
		for (int i = st; i <= e; i++) {
			if (ll[idxl] < rr[idxr]) {

			}
		}
		return ans;
	}

	public static class pair2 implements Comparable<pair2> {
		int a;
		int idx;

		pair2(int a, int i) {
			this.a = a;
			idx = i;
		}

		public String toString() {
			return a + " " + idx;
		}

		@Override
		public int compareTo(pair2 o) {
			// TODO Auto-generated method stub
			return idx - o.idx;
		}
	}

	static long inver(long x) {
		int a = (int) x;
		long e = (mod - 2);
		long res = 1;
		while (e > 0) {
			if ((e & 1) == 1) {
				// System.out.println(res*a);
				res = (int) ((1l * res * a) % mod);
			}
			a = (int) ((1l * a * a) % mod);
			e >>= 1;
		}
		// out.println(res+" "+x);
		return res % mod;
	}

	static int atMostSum(int arr[], int n, int k) {
		int sum = 0;
		int cnt = 0, maxcnt = 0;

		for (int i = 0; i < n; i++) {

			// If adding current element doesn't
			// cross limit add it to current window
			if ((sum + arr[i]) <= k) {
				sum += arr[i];
				cnt++;
			}

			// Else, remove first element of current
			// window and add the current element
			else if (sum != 0) {
				sum = sum - arr[i - cnt] + arr[i];
			}

			// keep track of max length.
			maxcnt = Math.max(cnt, maxcnt);
		}
		return maxcnt;
	}

	public static int[] longestSubarray(int[] inp) {
		// array containing prefix sums up to a certain index i
		int[] p = new int[inp.length];
		p[0] = inp[0];
		for (int i = 1; i < inp.length; i++) {
			p[i] = p[i - 1] + inp[i];
		}

		// array Q from the description below
		int[] q = new int[inp.length];
		q[inp.length - 1] = p[inp.length - 1];
		for (int i = inp.length - 2; i >= 0; i--) {
			q[i] = Math.max(q[i + 1], p[i]);
		}
		int a = 0;
		int b = 0;
		int maxLen = 0;
		int curr;
		int[] res = new int[] { -1, -1 };
		while (b < inp.length) {
			curr = a > 0 ? q[b] - p[a - 1] : q[b];
			if (curr >= 0) {
				if (b - a > maxLen) {
					maxLen = b - a;
					res = new int[] { a, b };
				}
				b++;
			} else {
				a++;
			}
		}
		return res;
	}

	static void factor(int n) {
		if (si[n] == n) {
			f.add(n);
			return;
		}
		f.add(si[n]);
		factor(n / si[n]);
	}

	static void seive() {
		si = new int[100001];
		primes = new ArrayList<>();
		int N = 100001;
		si[1] = 1;
		for (int i = 2; i < N; i++) {
			if (si[i] == 0) {
				si[i] = i;
				primes.add(i);
			}
			for (int j = 0; j < primes.size() && primes.get(j) <= si[i] && (i * primes.get(j)) < N; j++)
				si[primes.get(j) * i] = primes.get(j);

		}
	}

	static class unionfind {
		int[] p;
		int[] size;
		int jum;

		unionfind(int n) {
			p = new int[n];
			size = new int[n];

			for (int i = 0; i < n; i++) {
				p[i] = i;
			}
			jum = n;
			Arrays.fill(size, 1);
		}

		int findSet(int v) {
			if (v == p[v])
				return v;
			return p[v] = findSet(p[v]);
		}

		boolean sameSet(int a, int b) {
			a = findSet(a);
			b = findSet(b);
			if (a == b)
				return true;
			return false;
		}

		int max() {
			int max = 0;
			for (int i = 0; i < size.length; i++)
				if (size[i] > max)
					max = size[i];
			return max;
		}

		void combine(int a, int b) {
			a = findSet(a);
			b = findSet(b);
			if (a == b)
				return;
			jum--;
			if (size[a] > size[b]) {
				p[b] = a;
				size[a] += size[b];

			} else {
				p[a] = b;
				size[b] += size[a];
			}
		}
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

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

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

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

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

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}