Problem: You are given a tree (a graph with n vertices and n - 1 edges in which it's possible to reach any vertex from any other vertex using only its edges).

A vertex can be destroyed if this vertex has even degree. If you destroy a vertex, all edges connected to it are also deleted.

Destroy all vertices in the given tree or determine that it is impossible.

Input

The first line contains integer n (1 ≤ n ≤ 2·105) — number of vertices in a tree.

The second line contains n integers p1, p2, ..., pn (0 ≤ pi ≤ n). If pi ≠ 0 there is an edge between vertices i and pi. It is guaranteed that the given graph is a tree.

Output

If it's possible to destroy all vertices, print "YES" (without quotes), otherwise print "NO" (without quotes).

If it's possible to destroy all vertices, in the next n lines print the indices of the vertices in order you destroy them. If there are multiple correct answers, print any.

Examples

Input

5
0 1 2 1 2


Output

YES
1
2
3
5
4


Input

4
0 1 2 3


Output

NO

Note

In the first example at first you have to remove the vertex with index 1 (after that, the edges (1, 2) and (1, 4) are removed), then the vertex with index 2 (and edges (2, 3) and (2, 5) are removed). After that there are no edges in the tree, so you can remove remaining vertices in any order.

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Solution (in JAVA):

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

/**
 * @author Don Li
 */
public class DestructionTree3 {
    
    int N = (int) 2e5 + 10;
    
    int n;
    int[][] G;
    int[] sz = new int[N], par = new int[N], even = new int[N];
    
    void solve() {
        n = in.nextInt();
        
        if (n % 2 == 0) {
            out.println("NO");
            return;
        }
        
        int[] fr = new int[n - 1], to = new int[n - 1];
        for (int i = 0, j = 0; i < n; i++) {
            int p = in.nextInt() - 1;
            if (p != -1) {
                fr[j] = p;
                to[j++] = i;
            }
        }
        G = build_graph(n, fr, to);
        
        dfs(0, -1);
        
        int[] q = new int[n]; boolean[] inq = new boolean[n];
        int qh = 0, qt = 0;
        for (int i = 0; i < n; i++) {
            if (even[i] == 0) {
                q[qt++] = i;
                inq[i] = true;
            }
        }
        while (qh < qt) {
            int u = q[qh++];
            for (int v : G[u]) {
                if (inq[v]) continue;
                int comp_sz = u == par[v] ? n - sz[v] : sz[u];
                if (comp_sz % 2 == 0) even[v]--;
                if (even[v] == 0) {
                    q[qt++] = v;
                    inq[v] = true;
                }
            }
        }
    
        out.println("YES");
        for (int u : q) out.println(u + 1);
    }
    
    void dfs(int u, int p) {
        sz[u] = 1;
        par[u] = p;
        for (int v : G[u]) {
            if (v != p) {
                dfs(v, u);
                if (sz[v] % 2 == 0) even[u]++;
                sz[u] += sz[v];
            }
        }
        if (p != -1 && (n - sz[u]) % 2 == 0) even[u]++;
    }
    
    int[][] build_graph(int n, int[] from, int[] to) {
        int[][] G = new int[n][];
        int[] cnt = new int[n];
        for (int i = 0; i < from.length; i++) {
            cnt[from[i]]++;
            cnt[to[i]]++;
        }
        for (int i = 0; i < n; i++) G[i] = new int[cnt[i]];
        for (int i = 0; i < from.length; i++) {
            G[from[i]][--cnt[from[i]]] = to[i];
            G[to[i]][--cnt[to[i]]] = from[i];
        }
        return G;
    }
    
    public static void main(String[] args) {
        in = new FastScanner(new BufferedReader(new InputStreamReader(System.in)));
        out = new PrintWriter(System.out);
        new DestructionTree3().solve();
        out.close();
    }
    
    static FastScanner in;
    static PrintWriter out;
    
    static class FastScanner {
        BufferedReader in;
        StringTokenizer st;
        
        public FastScanner(BufferedReader in) {
            this.in = in;
        }
        
        public String nextToken() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(in.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        
        public int nextInt() {
            return Integer.parseInt(nextToken());
        }
        
        public long nextLong() {
            return Long.parseLong(nextToken());
        }
        
        public double nextDouble() {
            return Double.parseDouble(nextToken());
        }
    }
}