Given an equation, represented by words on the left side and the result on the right side.

You need to check if the equation is solvable under the following rules:

• Each character is decoded as one digit (0 - 9).
• No two characters can map to the same digit.
• Each words[i] and result are decoded as one number without leading zeros.
• Sum of numbers on the left side (words) will equal to the number on the right side (result).

Return true if the equation is solvable, otherwise return false.

 

Example 1:

Input: words = ["SEND","MORE"], result = "MONEY"
Output: true
Explanation: Map 'S'-> 9, 'E'->5, 'N'->6, 'D'->7, 'M'->1, 'O'->0, 'R'->8, 'Y'->'2'
Such that: "SEND" + "MORE" = "MONEY" ,  9567 + 1085 = 10652

Example 2:

Input: words = ["SIX","SEVEN","SEVEN"], result = "TWENTY"
Output: true
Explanation: Map 'S'-> 6, 'I'->5, 'X'->0, 'E'->8, 'V'->7, 'N'->2, 'T'->1, 'W'->'3', 'Y'->4
Such that: "SIX" + "SEVEN" + "SEVEN" = "TWENTY" ,  650 + 68782 + 68782 = 138214

Example 3:

Input: words = ["LEET","CODE"], result = "POINT"
Output: false
Explanation: There is no possible mapping to satisfy the equation, so we return false.
Note that two different characters cannot map to the same digit.

 

Constraints:

• 2 <= words.length <= 5
• 1 <= words[i].length, result.length <= 7
• words[i], result contain only uppercase English letters.
• The number of different characters used in the expression is at most 10.