The Human Development Index ($$\text{HDI}$$) of the United Nations is a composite statistic of life expectancy, education, and income indices in a certain country or area. The index was developed in 1990 by the Pakistani economist Mahbub ul Haq¹ and has been used since 1993 by the UNDP² in its yearly report. Norway is often at the first place. In 2016, the Netherlands took eighth place and Belgium could be found in 14^th place. At the bottom of the list are the African countries Chad, Central-African Republic and Niger.

The index measures the average performance of a country, divided in three categories: 

• national health: measured by the Life Expectancy Index ($$\text{LEI}$$) which expresses the mean life expectancy at birth \[\text{LEI} = \frac{\text{LE} - 20}{82.3 - 20}\,\] where $$\text{LE}$$ (Life Expectancy) represents the life expectancy at birth

• knowledge: measured by the Education Index ($$\text{EI}$$) which is a measure for illiteracy and the parts of the population that are in primary, secondary or tertiary education \[\text{EI} = \frac{\sqrt{\text{MYSI}\cdot\text{EYSI}}}{0.951}\;\] The Mean Years of Schooling Index ($$\text{MYSI}$$) is given by \[\text{MYSI} = \frac{\text{MYS}}{13.2}\,\] where $$\text{MYS}$$ (Mean Years of Schooling) is the average years of schooling for a 25-year-old (years that a 25-year-old person or older has spent in schools), and the Expected Years of Schooling Index ($$\text{EYSI}$$) is given by \[\text{EYSI} = \frac{\text{EYS}}{20.6}\,\] where $$\text{EYS}$$ (Expected Years of Schooling) represents the expected years of schooling for a 5-year-old (years that a 5-year-old child will spend with his education in his whole life)

• standard of living: measured by the income index ($$\text{II}$$) which expresses the gross national product per head of the population in purchasing power parity in dollars \[\text{II} = \frac{\ln(\text{GNIpc}) - \ln(100)}{\ln(107721) - \ln(100)}\,\] where $$\text{GNIpc}$$ (Gross National Income at purchasing power parity per capita) represents the gross national income per capita, and $$\ln$$ represents the natural logarithm³

Finally, the $$\text{HDI}$$ is the geometric mean⁴ of the previous three normalized indices: \[\text{HDI} = \sqrt[3]{\text{LEI}\cdot\text{EI}\cdot\text{II}}\]

Input

Five lines, the first of which contains the name of a country. This is followed by four lines containing the following information about the country:

• life expectancy at birth ($$\text{LE}$$)

• mean years of schooling for a 25-year-old ($$\text{MYS}$$)

• expected years of schooling for a 5-year-old ($$\text{EYS}$$)

• gross national income per capita ($$\text{GNIpc}$$)

These values are all expressed as floating point numbers.

Output

A single line containing the text

The HDI of country is 0.000.

where country must be replaced by the name of the country as read from input, and 0.000 must be replaced by the computed Human Development Index of the country. The $$\text{HDI}$$ must be formatted as a floating point number, rounded off to three decimal digits.

Example

Input:

Belgium
80.548
10.86875064
16.2
39470.90422

Output:

The HDI of Belgium is 0.890.

Resources

• Human Development Report 2016. UNDP. ⁵

• Human Development Report 2020. UNDP. ⁶