Context: Already during the later stages of the war, when the Commonwealth army moved from Smolensk to Bely, a new threat begun to loom on the southern borders, where the Ottoman Empire was massing an invasion force. Thus Władysław began redirecting his reinforcements to that theater. Later that year, the Commonwealth forces under Stanisław Koniecpolski scored a victory in the south, ending a war against the Ottomans. Both sides introduced new tactics, units and equipment based on Western models, but the Polish-Lithuanian forces proved more adept with these innovations than the Russians. However, the main factors that kept the Russians from winning were the delay in moving siege artillery to Smolensk and the severe disruption of Russian supply lines by Polish cavalry. A scapegoat was nevertheless needed: Mikhail Shein was accused of treason and, together with his second-in-command Artemy Izmaylov and the latter's son Vasily, executed in Moscow on April 28, 1634. Learning from this defeat, the Russians would adopt new and more successful tactics in the Polish-Russian War . After the war, Władysław gave the Russians the border town of Serpeysk and nearby territories, hoping to persuade the Tsar to join in an anti-Swedish alliance. However, the king was ultimately unable to overcome objections from the Polish-Lithuanian Sejm, who were unwilling to fight Sweden after the Treaty of Sztumska Wieś. The Russians, unable to see benefit in such an alliance, were also unenthusiastic, and the proposed alliance came to nothing. The war cost the Commonwealth treasury about 4,300,000 zloties. The Battle of Smolensk is commemorated on the Tomb of the Unknown Soldier, Warsaw, with the inscription "SMOLENSK 18 X 1632-25 II 1634".

Question: How many kingdoms did the king approach to form an anti-Swedish alliance?

Answer:
2