convert a string of a math formula to Object Tree in Javascript?

a function that converts a math string passed as a prop (with the operations +, -, /, *)
by returning an object that contains pieces of the math string, in an ordered/better way easier to loop on it then.

test cases if you need them:

Example 1: Basic Math (same operation)

N	Input (string)	Output (object)
1	1	{ values: [1], operation: null }
2	1+1	{ values: [1,1], operation: "+" }
3	1+2+3	{ values: [1,2,3], operation: "+" }
4	3-2-1	{ values: [3,2,1], operation: "-" }
5	10*80	{ values: [10,80], operation: "*" }
6	100/10	{ values: [100,10], operation: "/" }

Example 2: Formula with 2 operations

➡️ + and - samples

N1

input: 1+1-1

output:

{
    values: [
      {
        values: [1, 1],
        operation: "+",
      },
      1,
    ],
    operation: "-",
};

N2

input: 3+2-1+5

output:

{
    values: [
      {
        values: [
          {
            values: [3, 2],
            operation: "+",
          },
          1,
        ],
        operation: "-",
      },
      5,
    ],
    operation: "+",
};

N3

input: 3+2-1+5+10+7

output:

{
    values: [
      {
        values: [
          {
            values: [3, 2],
            operation: "+",
          },
          1,
        ],
        operation: "-",
      },
      5,
      10,
      7
    ],
    operation: "+",
};

➡️ + and / samples

N4

input: 1+2/3

output:

{
    values: [
      1,
      {
        values: [2, 3],
        operation: "/",
      },
    ],
    operation: "+",
};

N5

input: 2/3+1

output:

{
    values: [
      {
        values: [2, 3],
        operation: "/",
      },
      1,
    ],
    operation: "+",
};

N6

input: 1/2+3/4+5/6

output:

{
    values: [
      {
        values: [1, 2],
        operation: "/",
      },
      {
        values: [3, 4],
        operation: "/",
      },
      {
        values: [5, 6],
        operation: "/",
      },
    ],
    operation: "+",
};

N7

input: 1/2/3/4/5+6+7+8/9+10/11

output:

{
    values: [
      {
        values: [1, 2, 3, 4, 5],
        operation: "/",
      },
      6,
      7,
      {
        values: [8, 9],
        operation: "/",
      },
      {
        values: [10, 11],
        operation: "/",
      },
    ],
    operation: "+",
};

➡️ / and - samples

N8

input: 1-2/3

output:

{
    values: [
      1,
      {
        values: [2, 3],
        operation: "/",
      },
    ],
    operation: "-",
};

➡️ / and * samples

N9

input: 10/2*5

output:

{
    values: [
      {
        values: [10, 2],
        operation: "/",
      },
      5,
    ],
    operation: "*",
};

Example 3: Formula with 4 operations

N1

input: 10/2*5+1-1*5/3+2*4

output:

{
    values: [
      {
        values: [
          {
            values: [10, 2],
            operation: "/",
          },
          5,
        ],
        operation: "*",
      },
      1,
      {
        values: [
          {
            values: [-1, 5],
            operation: "*",
          },
          3,
        ],
        operation: "/",
      },
      {
        values: [2, 4],
        operation: "*",
      },
    ],
    operation: "+",
};

Example 4: Formula with () parenthesis

...