Problem: Consider a rooted tree. A rooted tree has one special vertex called the root. All edges are directed from the root. Vertex u is called a child of vertex v and vertex v is called a parent of vertex u if there exists a directed edge from v to u. A vertex is called a leaf if it doesn't have children and has a parent.

Let's call a rooted tree a spruce if its every non-leaf vertex has at least 3 leaf children. You are given a rooted tree, check whether it's a spruce.

The definition of a rooted tree can be found [here](https://goo.gl/1dqvzz).

Input

The first line contains one integer n — the number of vertices in the tree (3 ≤ n ≤ 1 000). Each of the next n - 1 lines contains one integer pi (1 ≤ i ≤ n - 1) — the index of the parent of the i + 1-th vertex (1 ≤ pi ≤ i).

Vertex 1 is the root. It's guaranteed that the root has at least 2 children.

Output

Print "Yes" if the tree is a spruce and "No" otherwise.

Examples

Input

4
1
1
1


Output

Yes


Input

7
1
1
1
2
2
2


Output

No


Input

8
1
1
1
1
3
3
3


Output

Yes

Note

The first example:

<image>

The second example:

<image>

It is not a spruce, because the non-leaf vertex 1 has only 2 leaf children.

The third example:

<image>

Solution (in JAVA):

Solution:
var n = +readline(); 
//+prompt("Enter kol verwun");
var koli4estvoVerwun = [n];

var roditelInex = 0;
var dannajaVetka;
var roditelVetka;
var mainVerwuna;
var verwuna;

koli4estvoVerwun[0] = {
                      roditel: null,
                      listkov: 0,
                      esListom: true
                      }

    function findRes(data) {
for (var i = 0; i < n; i++) {
verwuna = data[i];
if (!verwuna.esListom && verwuna.listkov < 3) {
return 'No';
} 
}
return 'Yes';
}

for (var i = 1; i < n; i++) {
    roditelInex = +readline() - 1;
    //+prompt("data") - 1;
    if (!koli4estvoVerwun[i]) {
        koli4estvoVerwun[i] = {
                              roditel: roditelInex,
                              listkov: 0,
                              esListom: true         
                              };
    }

dannajaVetka = koli4estvoVerwun[i];

if (!koli4estvoVerwun[roditelInex]) {
    koli4estvoVerwun[roditelInex] = {
        roditel: null,
        listkov: dannajaVetka.esListom ? 1 : 0,
        esListom: false
    };
} else {

roditelVetka = koli4estvoVerwun[roditelInex];
if (roditelVetka.esListom) {
    roditelVetka.esListom = false;

    mainVerwuna = koli4estvoVerwun[roditelVetka.roditel];
    if (mainVerwuna) {
        mainVerwuna.listkov = Math.max(0 , mainVerwuna.listkov -1);
    }
}
if (dannajaVetka.esListom) {
    roditelVetka.listkov++;
}
}
}
print(findRes(koli4estvoVerwun));
//alert(findRes(koli4estvoVerwun));