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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const long long MAXN = 2e5 + 100;
const long long INF = 1e18;
const long long MOD = 1e9 + 7;
struct Edge {
  long long from, to, nxt;
} edge[MAXN * 2];
long long eidx;
long long head[MAXN];
void addedge(long long from, long long to) {
  edge[eidx].from = from;
  edge[eidx].to = to;
  edge[eidx].nxt = head[from];
  head[from] = eidx++;
}
void einit() {
  eidx = 0;
  memset(head, -1, sizeof head);
}
long long wa[MAXN];
void dfs(long long u, long long fa) {
  for (long long i = head[u]; i != -1; i = edge[i].nxt) {
    long long v = edge[i].to;
    if (v == fa) continue;
    dfs(v, u);
    wa[u] += !wa[v];
  }
  wa[u] %= 2;
}
std::vector<long long> ans;
void del(long long u, long long fa) {
  for (long long i = head[u]; i != -1; i = edge[i].nxt) {
    long long v = edge[i].to;
    if (v == fa) continue;
    if (wa[v]) del(v, u);
  }
  ans.push_back(u);
  for (long long i = head[u]; i != -1; i = edge[i].nxt) {
    long long v = edge[i].to;
    if (v == fa) continue;
    if (!wa[v]) del(v, u);
  }
}
void init() { memset(wa, 0, sizeof wa); }
int main(int argc, char const *argv[]) {
  einit();
  init();
  long long n;
  scanf("%lld", &n);
  for (int i = 1; i <= n; ++i) {
    long long p;
    scanf("%lld", &p);
    if (p == 0) continue;
    addedge(i, p);
    addedge(p, i);
  }
  dfs(1, -1);
  if (wa[1]) {
    puts("NO");
    return 0;
  }
  del(1, -1);
  puts("YES");
  for (auto v : ans) {
    printf("%lld\n", v);
  }
  return 0;
}