You are given the `root` of a binary tree with `n` nodes where each `node` in the tree has `node.val` coins. There are `n` coins in total throughout the whole tree.

In one move, we may choose two adjacent nodes and move one coin from one node to another. A move may be from parent to child, or from child to parent.

Return _the **minimum** number of moves required to make every node have **exactly** one coin_.

**Example 1:**

**Input:** root = \[3,0,0\]
**Output:** 2
**Explanation:** From the root of the tree, we move one coin to its left child, and one coin to its right child.

**Example 2:**

**Input:** root = \[0,3,0\]
**Output:** 3
**Explanation:** From the left child of the root, we move two coins to the root \[taking two moves\]. Then, we move one coin from the root of the tree to the right child.

**Constraints:**

*   The number of nodes in the tree is `n`.
*   `1 <= n <= 100`
*   `0 <= Node.val <= n`
*   The sum of all `Node.val` is `n`.


def decode_permutation(s: str):
    n = len(s)
    perm = [0] * (n + 1)
    next_zero, next_one = 0, n

    for c in s:
        if c == '0':
            perm[next_zero] = next_one
            next_zero += 1
            next_one -= 1
        else:
            perm[next_one] = next_zero
            next_one -= 1
            next_zero += 1

    perm[next_zero] = next_one
    return perm
