import pandas as pd

# Define the original DataFrame
df = pd.DataFrame({
    'Name': ['food1', 'food2', 'food3'],
    'US': [1, 1, 0],
    'Canada': [5, 9, 6],
    'Japan': [7, 10, 5]
})

# Define the desired output
desired_output = pd.DataFrame({
    'Name': ['food1', 'food2', 'food3'],
    'US': [1, None, None],
    'Canada': [None, 9, None],
    'Japan': [None, None, 5]
}, index=[0, 1, 2])

# Define a function to create the desired output
def create_desired_output(df):
    # Melt the DataFrame
    melted_df = pd.melt(df, id_vars='Name', var_name='ctry', value_name='value')
    
    # Merge with the original DataFrame and set Corr..Name as the index
    merged_df = melted_df.set_index('Corr..Name')['value'].rename({0: 'US', 1: 'Canada', 2: 'Japan'}).reset_index()
    
    # Rename the columns to match the desired output
    result_df = merged_df.rename(columns={'US': 'US', 'Canada': 'Canada', 'Japan': 'Japan'})
    
    return result_df

# Apply the function to create the desired output
desired_output = create_desired_output(df)

# Print the final answer
print(desired_output)