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# Verify Preorder Serialization of a Binary Tree

One way to serialize a binary tree is to use pre-order traversal. When we encounter a non-null node, we record the node's value. If it is a null node, we record using a sentinel value such as`#`.

```
     _9_
    /   \
   3     2
  / \   / \
 4   1  #  6
/ \ / \   / \
# # # #   # #
```

For example, the above binary tree can be serialized to the string`"9,3,4,#,#,1,#,#,2,#,6,#,#"`, where`#`represents a null node.

Given a string of comma separated values, verify whether it is a correct preorder traversal serialization of a binary tree. Find an algorithm without reconstructing the tree.

Each comma separated value in the string must be either an integer or a character`'#'`representing`null`pointer.

You may assume that the input format is always valid, for example it could never contain two consecutive commas such as`"1,,3"`.

## Example

**Example 1:**

```
Input: "9,3,4,#,#,1,#,#,2,#,6,#,#"
Output: true
```

**Example 2:**

```
Input: "1,#"
Output: false
```

**Example 3:**

```
Input: "9,#,#,1"
Output: false
```

## Note

可以参考in-out degree的思想