You have been tasked with writing a program for a popular bank that will automate all its incoming transactions (transfer, deposit, and withdraw). The bank has n accounts numbered from 1 to n. The initial balance of each account is stored in a 0-indexed integer array balance, with the (i + 1)th account having an initial balance of balance[i].

Execute all the valid transactions. A transaction is valid if:

• The given account number(s) are between 1 and n, and
• The amount of money withdrawn or transferred from is less than or equal to the balance of the account.

Implement the Bank class:

• Bank(long[] balance) Initializes the object with the 0-indexed integer array balance.
• boolean transfer(int account1, int account2, long money) Transfers money dollars from the account numbered account1 to the account numbered account2. Return true if the transaction was successful, false otherwise.
• boolean deposit(int account, long money) Deposit money dollars into the account numbered account. Return true if the transaction was successful, false otherwise.
• boolean withdraw(int account, long money) Withdraw money dollars from the account numbered account. Return true if the transaction was successful, false otherwise.

Example 1:

Input
["Bank", "withdraw", "transfer", "deposit", "transfer", "withdraw"]
[[[10, 100, 20, 50, 30]], [3, 10], [5, 1, 20], [5, 20], [3, 4, 15], [10, 50]]
Output
[null, true, true, true, false, false]

Explanation
Bank bank = new Bank([10, 100, 20, 50, 30]);
bank.withdraw(3, 10);    // return true, account 3 has a balance of $20, so it is valid to withdraw $10.
                         // Account 3 has $20 - $10 = $10.
bank.transfer(5, 1, 20); // return true, account 5 has a balance of $30, so it is valid to transfer $20.
                         // Account 5 has $30 - $20 = $10, and account 1 has $10 + $20 = $30.
bank.deposit(5, 20);     // return true, it is valid to deposit $20 to account 5.
                         // Account 5 has $10 + $20 = $30.
bank.transfer(3, 4, 15); // return false, the current balance of account 3 is $10,
                         // so it is invalid to transfer $15 from it.
bank.withdraw(10, 50);   // return false, it is invalid because account 10 does not exist.

Constraints:

• n == balance.length
• 1 <= n, account, account1, account2 <= 105
• 0 <= balance[i], money <= 1012
• At most 104 calls will be made to each function transfer, deposit, withdraw.