Contrast Auditor

Story

The design system review is tomorrow and nobody has checked whether the palette is readable. Instead of pasting colours into a website one by one, you write an auditor that reads many colour pairs and reports the contrast ratio and the WCAG verdicts for each.

The formula

For a colour #RRGGBB (a three-digit #RGB colour means every digit is doubled, so #0af is #00aaff; hex letters may be upper or lower case):

1. Take each channel v (0 to 255) and compute c = v / 255.
2. Linearise it: lin = c / 12.92 if c <= 0.04045, otherwise lin = ((c + 0.055) / 1.055) ^ 2.4.
3. Relative luminance: L = 0.2126 * R + 0.7152 * G + 0.0722 * B using the three linearised channels.
4. Contrast ratio: (L_lighter + 0.05) / (L_darker + 0.05). It is always between 1 and 21, and it does not matter which of the two colours is the text.

The verdicts

• AA: normal text needs a ratio of at least 4.5.
• AA-large: large text needs a ratio of at least 3.
• AAA: normal text needs a ratio of at least 7.

Decide every verdict from the exact, unrounded ratio. Only the printed ratio is rounded.

Input

The first line holds N (1 ≤ N ≤ 100). Each of the next N lines holds two colours, the foreground and the background, separated by a space.

Output

N lines: <ratio> <AA> <AA-large> <AAA>, with the ratio rounded to two decimals and each verdict printed as PASS or FAIL. The ratio is compared with a tolerance of 0.006.

Example

Input:

2
#000000 #ffffff
#777777 #ffffff

Output:

21.00 PASS PASS PASS
4.48 FAIL PASS FAIL

Black on white is the maximum, 21:1. Mid grey #777777 on white is just below the 4.5:1 line, so it fails AA for normal text but is fine for large text.

2
#000000 #ffffff
#777777 #ffffff