Translate the following question to SQL: Show the minimum amount of transactions whose type code is "PUR" and whose share count is bigger than 50.

Schema: CREATE TABLE Investors (
    investor_id INTEGER   PRIMARY KEY,
    Investor_details VARCHAR(255)
);

CREATE TABLE Lots (
    lot_id INTEGER   PRIMARY KEY,
    investor_id INTEGER NOT NULL,
    lot_details VARCHAR(255),
    FOREIGN KEY (investor_id) REFERENCES Investors(investor_id)
);

CREATE TABLE Ref_Transaction_Types (
    transaction_type_code VARCHAR(10)   PRIMARY KEY,
    transaction_type_description VARCHAR(80) NOT NULL,
    UNIQUE (transaction_type_code)
);

CREATE TABLE Transactions (
    transaction_id INTEGER   PRIMARY KEY,
    investor_id INTEGER NOT NULL,
    transaction_type_code VARCHAR(10) NOT NULL,
    date_of_transaction DATETIME,
    amount_of_transaction DECIMAL(19,4),
    share_count VARCHAR(40),
    other_details VARCHAR(255),
    FOREIGN KEY (transaction_type_code) REFERENCES Ref_Transaction_Types(transaction_type_code),
    FOREIGN KEY (investor_id) REFERENCES Investors(investor_id)
);

CREATE TABLE Sales (
    sales_transaction_id INTEGER   PRIMARY KEY,
    sales_details VARCHAR(255),
    FOREIGN KEY (sales_transaction_id) REFERENCES Transactions(transaction_id)
);

CREATE TABLE Purchases (
    purchase_transaction_id INTEGER NOT NULL,
    purchase_details VARCHAR(255) NOT NULL,
    FOREIGN KEY (purchase_transaction_id) REFERENCES Transactions(transaction_id)
);

CREATE TABLE Transactions_Lots (
    transaction_id INTEGER NOT NULL,
    lot_id INTEGER NOT NULL,
    FOREIGN KEY (transaction_id) REFERENCES Transactions(transaction_id),
    FOREIGN KEY (lot_id) REFERENCES Lots(lot_id)
);
user
SELECT min(amount_of_transaction) FROM TRANSACTIONS WHERE transaction_type_code  =  "PUR" AND share_count  >  50
assistant