Letter Combinations of a Phone Number LeetCode solution in Rust

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impl Solution {
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  pub fn letter_combinations(digits: String) -> Vec<String> {
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    if digits.is_empty() {
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      return vec![];
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    }
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    let phone_map = vec!["abc", "def", "ghi", "jkl", "mno", "pqrs", "tuv", "wxyz"];
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    let mut output = Vec::new();
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    fn backtrack(
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      combination: String,
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      next_digits: &str,
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      phone_map: &Vec<&str>,
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      output: &mut Vec<String>,
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    ) {
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      if next_digits.is_empty() {
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        output.push(combination);
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      } else {
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        let letters = phone_map[next_digits.chars().nth(0).unwrap() as usize - '2' as usize];
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        for letter in letters.chars() {
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          let new_combination = combination.clone() + &letter.to_string();
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          backtrack(new_combination, &next_digits[1..], phone_map, output);
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        }
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      }
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    }
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    backtrack(String::new(), &digits, &phone_map, &mut output);
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    output
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  }
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}