A debt tracking app records transactions showing who paid whom and how much. Each transaction includes a borrower, a lender, and an amount.

Given a list of transactions, determine the minimum number of transactions required to settle all the debts.

Example

Suppose the number of people (n) = 3, the number of transactions (m) = 4, and transactions = [[0, 1, 20], [1, 0, 5], [1, 2, 10], [2, 0, 10]].

Each transaction is represented as [from, to, amount], meaning:

• Person 0 owes person 1 $20
• Person 1 owes person 0 $5
• Person 1 owes person 2 $10
• Person 2 owes person 0 $10

After simplification, only one transaction is needed: Person 0 pays $15 to person 1.

Therefore, the minimum number of transactions required is 1.

Constraints

• 2 ≤ n ≤ 9
• 2 ≤ m ≤ 10^6
• 0 ≤ debt[i][0], debt[i][1] < n
• 1 ≤ debt[i][2] ≤ 10^9