Question: which battle took place first,  Battle of Belleau Wood or Operation Diadem ?

Context paragraphs:
Battle of Kuwait International Airport: The Battle of Kuwait International Airport occurred on February 27, 1991 during the 1st Gulf War.  It was a tank battle between the United States and Ba'athist Iraq.  Despite being a very large battle it is often overlooked compared to the other battles which took place during the war.  No less than elements of 18 divisions total participated in this battle.  U.S. Army Special Forces units and multiple Iraqi Commando units were also in theatre.  In reality the battle took place over a span of three days despite the primary battle at Kuwait International Airport lasting only one day.  Much of the combat actually took place en route to the airport.  The battle featured the "Reveille Engagement" which went on to become the biggest and fastest tank battle in United States Marine Corps' entire history.

Battle of Dalrigh: The Battle of Dalrigh, also known as the Battle of Dail Righ, Battle of Dalry or Battle of Strathfillan, was fought in the summer of 1306 between the army of King Robert I of Scotland against the Clan MacDougall of Argyll who were allies of Clan Comyn and the English.  It took place at the hamlet of Dalrigh (the "King's Field" in the Scottish Gaelic language) near Tyndrum in Perthshire, Scotland (not to be confused with Dalry, Ayrshire).  Bruce's army, reeling westwards after defeat by the English at the Battle of Methven, was intercepted and all but destroyed, with Bruce himself narrowly escaping capture.  The battle took place sometime between late July and early August, but the exact date is unknown.

Battle of the Allia: The Battle of the Allia was fought between the Senones (one of the Gallic tribes which had invaded northern Italy) and the Romans.  It was fought at the confluence of the rivers Tiber and Allia, eleven Roman miles (16 km) north of Rome.  The Romans were routed and subsequently the Senones sacked Rome.  The common date given for the battle is 390 BC.  This is based on the account of the battle by the Roman historian Livy and the Varronian Chronology, a Roman dating system.  The ancient Greek historian Polybius, who used a Greek dating system, derived the date 387/6 BC.  Plutarch wrote that the battle took place just after the summer solstice when the moon was near the full, a little more than three hundred and sixty years from the foundation of Rome.  That would be shortly after 393 BC.  Tacitus said that the battle took place the 15 before the Kalends of August, which is 18 July.

Battle of the Bay of Biscay: The Battle of the Bay of Biscay was a naval action that took place on 28 December 1943 during World War II as part of the Atlantic campaign.  The battle took place in the Bay of Biscay between two light cruisers of the British Royal Navy, and a destroyer and a torpedo boat flotilla of the German Kriegsmarine hoping to intercept and escort a blockade runner.  The battle was fought as part of the Allied Operation Stonewall which was to intercept German blockade runners off the west coast of France.  In the confused action that followed the two British cruisers HMS "Enterprise" and HMS "Glasgow" respectively sank "T-26", together with her sister ship "T-25" and the destroyer "Z27".

Battle of Belleau Wood: The Battle of Belleau Wood (1–26 June 1918) occurred during the German Spring Offensive in World War I, near the Marne River in France.  The battle was fought between the U.S. 2nd (under the command of Major General Omar Bundy) and 3rd Divisions along with French and British forces against an assortment of German units including elements from the 237th, 10th, 197th, 87th, and 28th Divisions.  The battle has become a key component of the lore of the United States Marine Corps.

USS Cole (DD-155): USS "Cole" (DD-155) was a "Wickes"-class destroyer in the United States Navy during World War II, later reclassified as AG-116.  She was the first ship named for Edward B. Cole, a USMC officer who died as a result of the wounds he received at the Battle of Belleau Wood.

Operation Diadem: Operation Diadem, also referred to as the Fourth Battle of Monte Cassino or, in Canada, the Battle of the Liri Valley, was an offensive operation undertaken by the Allies of World War II (U.S. Fifth Army and British Eighth Army in May 1944, as part of the Italian Campaign of World War II.  "Diadem" was supported by air attacks called Operation Strangle.  The opposing force was the German 10th Army.

Battle of Suoi Chau Pha: The Battle of Suoi Chau Pha (6 August 1967) was fought during the Vietnam War between Australian troops and the Viet Cong.  The battle took place during Operation Ballarat, an Australian search and destroy operation in the eastern Hat Dich area, north-west of Nui Dat in Phuoc Tuy province.  Following a covert insertion the day before which had caught a number of Viet Cong sentries by surprise, A Company, 7th Battalion, Royal Australian Regiment (7 RAR) had patrolled forward unaware of the presence of a large Viet Cong main force unit nearby.  Clashing with a reinforced company from the Viet Cong 3rd Battalion, 274th Regiment, a classic encounter battle ensued between two forces of roughly equal size.  Fought at close quarters in dense jungle amid a heavy monsoon rain, both sides suffered heavy casualties as neither was able to gain an advantage.  Finally, after a battle lasting several hours, the Australian artillery proved decisive and the Viet Cong were forced to withdraw, dragging many of their dead from the battlefield after having suffered crippling losses.

Battle of Cape Esperance: The Battle of Cape Esperance, also known as the Second Battle of Savo Island and, in Japanese sources, as the Sea Battle of Savo Island (サボ島沖海戦 ) , took place on 11–12 October 1942 in the Pacific campaign of World War II between the Imperial Japanese Navy and United States Navy.  The naval battle was the second of four major surface engagements during the Guadalcanal campaign and took place at the entrance to the strait between Savo Island and Guadalcanal in the Solomon Islands.  Cape Esperance ( ) is the northernmost point on Guadalcanal, and the battle took its name from this point.

Battle of Clitheroe: The Battle of Clitheroe was a battle between a force of Scots and English knights and men at arms which took place on 10 June 1138 during the period of The Anarchy.  The battle was fought on the southern edge of the Bowland Fells, at Clitheroe, Lancashire.  It took place in the course of an invasion of England by King David I of Scotland.  In the summer of 1138, King David split his army into two forces.  One of them, commanded by William fitz Duncan, Mormaer of Moray, marched into Lancashire.  There he harried Furness and Craven.  On 10 June, William fitz Duncan was met by a force of knights and men-at-arms.  A pitched battle took place and the result was that the English army was routed.  The battle was a prelude to the Battle of the Standard later in the summer, where the result was reversed.

Supporting paragraphs: Battle of Belleau Wood Operation Diadem
Answer: Battle of Belleau Wood