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- The amount of money withdrawn or transferred from is less than or equal to the balance of the account.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`.